Altius Lesson: Physics 4
Use the "packets of light" visualization to predict light behavior at the surface of a converging and diverging lens, and at the surface of a convexs and concave mirror. (a) What type of lens is found in the human eye? (b) In a magnifying glass? (Hint: It is NOT the one most people first assume.)
(a) The lens of the human eye is a converging lens. It creates a real image of the object onto the retina. (b) A magnifying glass is also a converging lens. Most students assume it would be a diverging lens because the rays that are spreading apart might seem like they would make the image appear larger. This thinking reflects a misconception about where images are formed. Your eye does not capture divergent rays and form an image based on how far apart those rays are—rather it traces those rays back to where it appears that the source of the rays would be. Also note that in a magnifying glass we see an upright image—even though converging lenses are said to create positive, real, INVERTED images. This is an example of the caveat given in bold in the lesson: When the object is inside the focal point it produces a negative, virtual, upright image. This is the case with a magnifying glass. In order to see the magnified image the object must be inside the focal point of the lens. This is also supported by the formula for magnification, which shows us that in order for the image to be magnified the distance between the object and the lens must be less than the distance between the observer (image) and the lens (M = -di/do).
Pitch is? Higher pitch sounds have higher or lower frequencies? Lower pitch sounds have higher or lower frequencies?
*Pitch is a musical term not a scientific term - higher frequencies - lower pitch sounds have lower frequencies.
Although the densities of solids are typically thousands of times higher than the densities of gases, the elastic moduli are even increased by an even larger factor. This property causes solids to? Sound (compression) waves in solids are therefore typically slower or faster?
- "spring back" extremely quickly following deformation - much faster than sound waves in gases
Object distances (do) are ALWAYS? Image distances (di) or focal point distances (f) are (+) if? Image distances (di) or focal point distances (f) are (-) if? The observer and object are on the same side for a? The observer and object are on the opposite side for a?
- + positive - they are on the same side as the observer - they are on the opposite side - mirror - lens
The refractive index of water is? What does this mean? Index of refraction formula? What do the variables represent?
- 1.33, meaning that light travels 1.33 times faster in a vacuum as it does in water. - c =speed of light in vacuum. - v = speed of light in substance.
An object is imaged by a convex lens. Assuming the object is outside the focal distance, the image formed will be: A) on the same side of the lens as the observer and virtual B) on the same side of the lens as the observer and real C) on the opposite side of the lens as the observer and virtual D) on the opposite side of the lens as the observer and real
- A converging lens can only form an NVU image if the object is within the focal distance. We are told it is not, so we know the image must be positive, real and inverted. Positive means it is on the same side as the observer, which makes answer B correct. The image must also be inverted.
Attenuation formula If person A is positioned three times as far from the source of a sound as person B, what will be the ratio of the intensity of the sound experienced by person A to that experienced by person B?
- A=4π r2 - The intensity of the sound will fall off according to: I = watts/4πr^2. Thus, by simple manipulation of this equation, we see that if the radius between the sound and person A is three times as great as the radius between the sound and person B, the intensity will be decreased by a factor of nine (9).
Diverging lens (concave, negative) produces what image? For objects that are far away, assume the light rays hitting the lens are?
- ALWAYS produces a negative, virtual, upright image - all parallel
Far sighted. Image is formed behind or infront of the retina?
- Able to focus clearly on distant objects, but not close objects - behind the retina
Sound resonance Resonance is when one object vibrates and causes?
- All objects have one or more natural frequencies at which they will vibrate when disturbed. Some objects produce a random array of different vibrational frequencies. Instruments produce orderly arrays called harmonics. - Another to vibrate at a certain frequency and if those frequencies happen to be one of its natural frequencies.
The intensity of any sound or mechanical wave is directly proportional to? What will be the change in frequency due to The Doppler effect when the source and observer are traveling the same speed?
- the amplitude squared and the frequency squared (i.e., I A2f2 ) - if the source and observer are traveling at the same speed there will be no Doppler effect. This is TRUE, if—and only if—they are both traveling in the same direction (notice that we used the term speed, the scalar, not velocity, the vector). If they were traveling away from each other at identical speeds there would certainly be a Doppler shift.
Visible light spectrum Place the following waves in order of decreasing frequency: gamma rays, ultraviolet, radio waves, x-rays, microwaves, infrared, visible light
390nm-700nm ROY G BIV In terms of frequency, gamma rays > x-rays > ultraviolet > visible light > infrared > microwaves > radio waves
magnification formula
:)
Near Sighted. Image is formed where?
Able to focus clearly on close objects, not on distant objects *image is formed in front of the retina
Dual nature of light: Particle
Light is made up of little particles that obey the laws of physics like other masses.
Phase Definition (wave)
is a relative measure of how closely two waves (typically with the same frequency) are oriented to one another in space, typically expressed in radians or degrees. Two waves that are "in phase" should cross the x-axis at the same point, but may have different amplitudes.
Why does the image move in front of or behind the retina for near- or far-sighted people as is described above? Draw some diagrams of a convex lens and try to figure it out. (Hint: It has something to do with the shape of the lens.)
- For a near-sighted person, the lens has too much focusing power (the focal length is too small). This causes the light to bend more than it should, and the image is formed closer to the lens than it should. See the second illustration for question #29, imagining that the rays are converging to the retina, and visualize what it would look like with more bending than expected. For a far-sighted person, the lens has too little focusing power (the focal length is too large). This causes the light to bend less than it should, and the image is formed farther from the lens than it should. See the second illustration for question #29, visualizing what it would look like with less bending than expected. A fully-functioning eye can accommodate a wide variety of incoming light angles because the ciliary muscles of the eye are capable of adjusting the curvature of the lens and therefore its focal point. As we age, however, we gradually lose this flexibility. In persons born with a near- or far-sighted condition the natural shape of the lens is not exactly what it needs to be for the focal point to land directly on the retina and the adjustment that would be necessary to bring the light into focus on the retina exceeds the limitations of the ciliary muscles. (Note: It is a bit more complicated than implied here, because the cornea actually bends light more than the lens itself. MCAT questions tend to ignore that complication. It does make sense, however, because LASIK corrective surgery does nothing to your lens—it reshapes your cornea!)
Intensity in decibels equation = At a soccer match, the sound level suddenly rises from 20 decibels to 60 decibels. How much louder (more intense) is the sound at the end of this increase?
- I is intensity of sound wave in W/m2 - Io is the threshold of human hearing ( 1 e-12 W/m2; always given) -The difference between 20 and 60 decibels is 40 decibels, or 4 factors of 10. Therefore the sound intensity has increased by a factor of 10,000.
Does the power of the human eye increase or decrease when the ciliary muscles contract?
- In upcoming biology lessons you will be required to learn that the flexing of the ciliary muscles results in an increase in the curvature of the lens. As the curvature of a lens increases, its focal point decreases. Because power is the inverse of focal length, we know that a more curved lens (i.e., contracted ciliary muscles) produces a shorter focal point and therefore a more powerful lens.
Intensity Definition (wave) The intensity of any sound or mechanical wave is _____ proportional to the amplitude squared and the frequency squared
- Intensity is defined as power per unit area. Waves have power (often called "sound power") because they transfer energy from one location to another within a specified time (a.k.a., energy flux). Power= Change in E / time - directly. I proportional A^2f^2
Summary of harmonics. Open open, or closed closed equation? Open closed harmonics equation?
- L = nλ/2 -L = nλ/4
Dual nature of light: Wave The frequency of any harmonic is equal to? The 1st overtone is NOT the same as? For oscillators with matching ends, the wavelength of the second harmonic equals ?
- Light acts as a wave. It defracts, refracts, reflects, and interferes. http://m.youtube.com/watch?v=DfPeprQ7oGc - n*fundamental frequency (e.g., if the first harmonic is exactly 200 Hz, the 2nd is 400 Hz, the 3rd is 600 Hz, etc.) - the 1st harmonic! - length of the string or pipe (λ = L)
To demonstrate the parallel rays assumption for distant objects, draw a set of parallel rays bending through a converging lens. Next to it, draw a similar diagram for rays coming from an object much closer to the lens (but still farther than one focal length away). What happens to the point where the rays converge?
- Parallel rays will all converge to the focal point. That's the definition of the focal point (See the left figure below). If the object is closer to the lens, the rays will not be able to bend enough to converge at the same spot. They will converge, or "focus" at a spot farther away. That is the image location, not the focal point. See the right figure below
A student blows into a pipe open at both ends and creates a fundamental frequency. He then increases his pitch gradually until he reaches the 2nd and 3rd harmonics. While the 3rd harmonic is resonating, the student puts his hand over one end of the pipe. To attain the 3rd harmonic for the new system, the student must: A) increase the frequency of the sound B) decrease the frequency of the sound C) maintain a constant frequency D) decrease the wavelength of the sound
- The 3rd harmonic for this pipe will have three nodes and three antinodes. When the student places his hand over the pipe, he creates a pipe open at one end and closed at the other. The third harmonic for this new system will have only two nodes and two antinodes. By drawing these harmonics on the same length of pipe we can see that the 3rd harmonic in the second case clearly has a longer wavelength—and hence a lower frequency. Answer B is therefore correct.
Critical angle and snells law How does dispersion account for the behavior of light passing through a prism? What color of light bends the least when entering a prism? The most?
- The classic example of dispersion is white light passing through a prism. For visible light traveling through glass longer wavelengths have smaller indices of refraction and therefore bend less than smaller wavelengths. This means red light bends the least, and violet light bends the most. This difference in refraction separates the white light into its colored components and produces a rainbow. - Red light bends the least. - Violet light bends the most
Important 5 Characteristics of Harmonics
- The frequency of the first harmonic is called the "fundamental frequency." Each additional harmonic has its own unique frequency and wavelength. - The frequency of any harmonic is equal to n*fundamental frequency (e.g., if the first harmonic is exactly 200 Hz, the 2nd is 400 Hz, the 3rd is 600 Hz, etc.) - Each harmonic always has one more node, and one more antinode, than the previous harmonic. - Overtones: The terms "1st overtone," "2nd overtone," etc., are sometimes used. The 1st overtone is NOT the same as the 1st harmonic! The first harmonic is called the fundamental frequency, the second harmonic is called the 1st overtone, the third harmonic is called the 2nd overtone, and so forth. - For oscillators with matching ends, the wavelength of the second harmonic equals the length of the string or pipe (λ = L)
What happens to frequency and wavelength when light refracts into a new medium?
- The frequency will not change as the wave moves from one medium to another. We like to think of the frequency as the permanent "identifier" of a wave. For example, you will often hear waves referred to as "a 400Hz wave, a 200Hz wave, etc." This makes sense because the frequency stays the same as it passes through different mediums. - The wavelength, however, must change from medium to medium (assuming they have different densities) because we know that the velocity of electromagnetic waves does NOT remain constant from medium to medium—it is generally higher in less dense mediums and lower in more dense mediums. According to v = fλ if frequency remains constant and velocity changes, wavelength must change. Because velocity increases in low index mediums, wavelength must also increase in low index mediums.
Attenuation is? Because intensity is measured per square meter, its magnitude decreases according to the?
- The gradual loss of intensity as a wave passes through a medium. In non dispersive mediums this is due to scattering (reflection) of some waves and absorption of wave energy. - area of the growing sphere (i.e., the m2 term increases, decreasing the intensity): A = 4πr2
Wavelength Definition (wave) For a more complex wave, the wavelength is?
- The length of one complete wave cycle. Crest to Crest or Trough to Trough. - the distance between points where the wave begins to repeat itself
Car A is traveling at 20m/s toward car B and car B is traveling toward car A at 15m/s. Car B honks its horn and car A perceives the frequency of that sound as f. After they pass one another, car B slows down to 5m/s and honks its horn again. What must the motion of car A be at that moment in order for the perceived frequency of the second horn to equal f?
- The original relative velocity described in the question was a 35m/s approach between source and observer. To match the exact frequency shift they must also be approaching one another at the same relative velocity in the second scenario. In the second scenario Car B is traveling 5 m/s away from car A, thus car A must turn around and travel TOWARD car B at a rate of 40m/s in order to experience the same perceived frequency from car B's horn. (This is the answer using our appropriate formulas; the correct answer" using the full-fledged formulas will be quite close to that value, but far more difficult to obtain.)
What is the photoelectric effect and how does it relate to the particle model of light?
- The photoelectric effect is the observation that electrons are ejected from a material when light of sufficiently high frequency is used—but not until a threshold frequency is reached. Einstein first published an explanation for these observations in the context of the particle nature of light. If light were purely a conventional wave, increasing the amplitude sufficiently high would always result in ejection of an electron—which is not seen. Instead, we observe that the energy of each individual photon (set by its frequency) must itself be high enough for an electron to be ejected. There is a one-to-one correspondence between photons and electrons.
Provide a conceptual definition for the particle and wave models of light.
- The wave model of light supposes that light is a wave. Young's Double Slit Experiment provides support for this model because only waves would show the diffraction and interference patterns necessary to create the characteristic light and dark bands. The particle model of light supposes that light is a particle. The photoelectric effect is the major support for this model. The two are reconciled by quantum mechanics: photons are described by "wave functions" which sometimes act as macroscopic waves and sometimes as macroscopic particles.
Standing waves What will be the result of adding two otherwise identical waves that are: a) 180 degrees out of phase, b) 360 degrees out of phase, c) 270 degrees out of phase?
- Two waves of identical frequencies moving through the same medium in opposite directions. Max constructive-antinodes and max destructive-nodes.*Does not itself propagate and no net transport of energy. - a) the waves will exactly cancel, b) 360 degrees out of phase is the same a 0 degrees out of phase, which is the same as being "in phase." Therefore the waves will add to one another to create a wave with an amplitude equal to the sum of the amplitudes of the two previous waves, c) There will be multiple areas of constructive and destructive interference, creating a new waveform with multiple crests and troughs.
Converging lens (convex, positive) produce what image? When the object is inside the focal point it produces?
- USUALLY produces a positive, real, inverted image. - a negative, virtual, upright image.
Wave speed through various mediums formula The elastic property is often called? The inertial property is? Wave A has twice the amplitude, one-half the wavelength, and three times the frequency of wave B. Which wave will travel with the greater velocity through an identical dispersive medium?
- V= sqrt (elastic/inertial) Wave speed is typically equal to the square root of an elastic property of the medium divided by an inertial propert - "modulus" - a type of density - Since velocity equals frequency times wavelength, the wave with the highest frequency x wavelength product will travel the fastest. That's wave A. (If the medium were non-dispersive, then the two waves would by definition travel the same speed. The frequency x wavelength would necessarily be the same in that case.)
Velocity of a wave on a string formula What property provides the restoring force in a string ? The inertial property is? Increased tension always increases? If the tension stays the same, a thicker string (increased mass per length) always ______ velocity?
- V=sqrt (T/u) - its tension - mass per unit length, the "linear mass density" - Velocity - Decreases
Single slit: Does diffraction still occur? Every point in the slit will act as? What is the fringe result? Perhaps surprisingly, a pattern of fringes can also be produced if the double-slit screen is replaced with a screen having only one slit. Provide possible explanations for this observation.
- Yes - as a source of spherical waves. - a very bright central fringe and much lighter bands on either side. - These waves interfere with each other just like the waves coming through each of the two slits in Young's experiment. However, the interference isn't as drastic as with a double-slit, and what results is a very bright central fringe and much lighter bands on either side.
Do Mechanical waves require a medium to propagate? Give an example of a transverse wave and longitudinal
- Yes; transfer energy only *Transverse (all the electromagnetic waves, audience waves, magnetic waves, surface waves, S earthquake waves, ultraviolet waves, wave in a string) *Longitudinal (sound waves, tsunami waves, earthquake P waves, ultra sounds, vibrations in gas, and oscillations in spring, internal water waves)
Youngs double slit experiment: For the experiment to work the light going through the middle screen must have the same ?
- Young shone a monochromatic light through a screen with a single slit in it. The purpose of this slit was to create coherent wavefronts (since lasers weren't around in Young's day). Behind the first screen he placed a second screen with two narrow, parallel slits. These created the diffraction pattern. Finally, behind the second screen he placed a third screen. Light traveled through the first two screens and formed alternating pattern of light and dark bands on the third screen. - frequency and polarization
Dispersion is?
- a change in index of refraction based on the frequency (or wavelength) of a wave. In a material with dispersion, different frequencies (or wavelengths) will be refracted to different angles, for the same incident angle. The classic example of dispersion is white light passing through a prism. For visible light traveling through glass longer wavelengths have smaller indices of refraction and therefore bend less than smaller wavelengths. This means red light bends the least, and violet light bends the most. This difference in refraction separates the white light into its colored components and produces a rainbow
Who has the more powerful lens, a person who is near-sighted or one who is far-sighted?
- a near-sighted person—because their lens has the shorter default focal length, also has the more powerful lens.
Production of sound Sound is always created by? AS A MECHANICAL WAVE, SOUND CANNOT PROPAGATE THROUGH?
- a vibrating medium. These vibrations propagate through liquids or solids, and generate pressure waves that propagate through gases such as air. - A VACUUM
What is the relative velocity in each of the following cases? a) observer has zero velocity, source is traveling toward the observer at 5m/s, b) observer and source are traveling in opposite directions, both at 5m/s, c) observer is traveling east at 5m/s, source is traveling east at 2m/s, d) observer and source are traveling toward one another, one at 5m/s and the other at 2m/s.
- a) 5m/s ; b) 10m/s ; c) 3m/s ; d) 7m/s
In order to be 100% in phase, two waves would have to have the same? The latter is important because two waves might share the first two variables in common and would therefore be in phase if started from the same point, but would NOT be in phase if started from? If they share the same frequency they must share the same
- frequency, wavelength, and timing of maxima/minima (which could be done if they share the same time/place of origin). - differnets times - period
A magnifying glass (when used as a magnifier) is positioned such that the object is inside or outside the focal distance? What kind of image does this produce? Volume, is a measure of?
- inside - a virtual, upright image on the opposite side of the glass - intensity
Intensity Intensity is proportional to?
- is a measure of power per unit area. Waves have power because they transport energy from one point to another in a given amount of time. - The square of the amplitude and the square of the frequency.
Velocity Definition (wave)
- is how fast the wave moves in space in m/s. It is given by v = fλ
Amplitude Definition (wave)
- is the "distance" between the equilibrium point and a crest, or between the equilibrium point and a trough. (Distance is in quotes because the units of amplitude are not necessarily meters. They would be, for a wave on a rope, but not, for example, for a voltage wave or the electric field component of a light wave. Those would have units of volts or volts/m, respectively.) It is NOT the total distance between crest and trough! That would be twice the amplitude
In what way does velocity of light change in different densities of mediums? Because velocity increases in low index mediums, wavelength must ? For total internal reflection to occur, the light must ?
- it is generally higher in less dense mediums and lower in more dense mediums - must also increase in low index mediums - the light must be passing from a higher index medium to a lower index medium.
Electromagnetic spectrum: Longer wavelength = ? Shorter wavelength = ? Which form of light has the greater velocity in a vacuum, gamma waves or radio waves?
- lower frequency = less energy - higher frequency = more energy All of the waves on the electromagnetic spectrum travel at the same speed in a vacuum, "c".
In general, all waves SLOW DOWN when they hit a less dense or denser medium? What is an exception to this? Thinking of the tire in the mud example, as a car enter a higher denser medium, the car will rotate more creating a smaller or larger angle of incidence?
- more dense - sound waves - smaller
What is refraction vs. diffraction?
- refraction is bending of light as it goes through a medium - Diffraction is tendency of light to spread out as it goes around a corner.
Concave mirrors For plane mirrors only, the image and the object will always be?
- same as converging lens - equal distances on either side of the mirror
Snells law formula is? What can be inferred about a material with an index of refraction of a) 0.9 and b) 1.5?
- see photo The index of refraction is a relative comparison of the speed of light in a vacuum (c) to the speed of light in that medium (v): n = c/v. Therefore, in order to get a value less than one, the speed of light in that medium would have to be greater than the speed of light in a vacuum which is only possible for circumstances beyond what the MCAT would be testing on. A value of 1.5 for n simply tells us that the medium has some density, and is more dense than air, which has a value for n that is very close to one.
Color Shifts White light can shift BLUE if? White light can shift RED if?
- the Doppler effect causes an increase in frequency (decrease in wavelength) - if Doppler effect caused a decrease in frequency (increase in wavelength)
Period Definition (wave)
- the amount of time required for one full wavelength to pass a fixed point (units = seconds).
For waves passing from higher index mediums into lower index mediums, the critical angle is? If an angle of 90° is exceeded what happens to refraction? The critical angle is? Snell's Law can be used to solve for the critical angle by?
- the angle of incidence for which the angle of refraction will be 90°. - refraction ceases and all waves are reflected back into the more dense medium—a phenomenon called "total internal reflection." - the angle of incidence above which the total internal reflection occurs - plugging in 90° for θ2: n1sinθ1 = n2sinθ2 → n1sinθ1 = n2sin90°→ sinθ1 = n2/n1. If the two indices of refraction are known, the unknown variable, θ1, would be the critical angle.
Angle of incidence is what in relation to the medium?
- the angle of incidence is the angle between a ray incident on a surface and the line perpendicular to the surface at the point of incidence
Refraction is?
- the bending of light at an interface between two mediums with different indices of refraction
Reflection is? Diffraction is?
- the bouncing of a wave off of an interface between two mediums. - the bending of a wave around a corner or obstacle
Total internal reflection For light crossing a boundary from a slower to a faster medium (like from glass or water into air), if the angle of refraction would be 90° or more, what happens to the incident light? Why does the wavelength of light change from medium to medium?
- the incident light does not enter the second medium at all—100% of the light is reflected off the boundary and back into the first medium. For total internal reflection to occur, the light must be passing from a higher index medium to a lower index medium. - velocity of electromagnetic waves does NOT remain constant from medium to medium
If the wavelength of the light emanating from the light source in Young's experiment was decreased, how would this affect the number of light and dark bands on the screen?
- the number of both would increase - The light and dark bands are created by interference between the two waves coming from the pinholes in the second board. If the wavelength of the light was very, very large, say bigger than the screen, then you would see no more than one band of interference, either completely dark or completely light. If we take this the other direction, to a very, very small wavelength, you would see tons of little light and dark bands. The key is that when two waves interfere, they do so in a repeating pattern whose distance between bands is proportional to the wavelength.
Frequency Definition (wave) Period and frequency are always inverses of each other?
- the number of wavelengths that pass a fixed point each second (units = 1/s or s-1 or Hertz [Hz]). - yes
Diffraction definition: How will increasing each of the following in Young's experiment change the distance between the fringes? a) wavelength, b) distance between the two slits, c) distance between the second and third screen.
- the tendency of light to spread out as it goes around a corner or through a slit. - Each answer is easily obtained by manipulation of the equation given: x = λL/d. This is a simplified version of an equation relating to Young's experiment called "the small angle approximation." a) increasing wavelength will increase the distance between fringes (x); b) increasing the distance between slits (d) will decrease the distance between fringes (x); c) increasing the distance between the second and third screen (L) will increase the distance between fringes.
Formulas for velocity of a wave in a gas? The elastic property is called? The inertial property is ? The bulk modulus turns out to be both directly proportional to both? For gases the velocity ends up having this temperature dependence?
- v = sqrt(B/ρ) - the "bulk modulus", B - normal density - density and temperature - v ~ sqrt(T)
For the first harmonic on a string attached at both ends, there are two nodes and one antinode. This will form how many waves? The wavelength of the first harmonic is how many times the length of the string?
- with two nodes and one anit node it will form one half of a wave - twice
The following formula is given solely to help you see relationships and to aid you in answering a specific question type the MCAT tends to ask about Young's experiment—namely, how will changes in wavelength, distance between the slits, etc. alter the pattern of fringes produced. What does each variable represent?
- x = λL/d - where x is the distance between fringes, λ is the wavelength of light used, d is the distance between the two slits, and L is the distance between the "double slit" and the final screen (strictly true only when x is much smaller than L).
The "ratio of the change in wavelength to the wavelength" means?
- Δλ/λ, the bottom variable is the original wavelength
Waves that displace the medium perpendicular to their direction of travel are? Waves that displace the medium parallel to their direction of travel are?Electromagnetic waves?
-Transverse - Longitudinal - No medium required; capable of propagating in a vacuum; transfer energy and momentum (visible light, microwaves, radio waves) *Transverse only
The 4 lens/mirror rules (1 lens system only)
1) Object distances (do) are ALWAYS (+) 2) Image distances (di) or focal point distances (f) are (+) if they are on the same side as the observer and (-) if they are on the opposite side. 3) The observer and object are on the same side for a mirror and on opposite sides for a lens (you have to be behind your glasses to see through them to view the object on the other side) 4) PRI / NVU: "Positive, Real, Inverted" and "Negative, Virtual, Upright" always stay together! You only need to establish one characteristic and you automatically know the other two!
Pipe closed at one end nodes and harmonics ?
1) One node and one antinode 2) gives odd harmonics only n=1,3,5...
5 Characteristics of Sound waves
1) Require a solid liquid or gas to act as a medium 2) Pass through solids by vibrating the solid itself 3) lose some amplitude when passing through a solid 4) increase in velocity when passing through a more dense material 5) medium determines velocity
Three key points with respect to the Doppler Formula
1) The variable V is relative velocity, NOT velocity of either object. 2) The variable c is 340m/s (sound) or 3e8m/s (light) 3) The answer is in CHANGE of frequency which is often not what is asked for This value must be added or subtracted from the initial value to get the actual value due to the Doppler effect. Add to the frequency (subtract from the wavelength) if the relative motion is towards each other; do the opposite if the relative motion is away from each other.
The three cardinal wave rules are?
1) Wave speed (v) is determined by the medium and sometimes (for dispersive) wavelength and frequency. 2) Frequency NEVER changes when a wave moves from medium to medium 3) Wavelength DOES change when wave moves from medium to medium
Both ends of a pipe open or closed nodes and harmonics are?
1) both nodes or antinodes 2) Gives all harmonics in n=1,2,3...
Thin lens equation (mirrors also)
1/f=1/di + 1/do
What is the decibel system? A 10-fold increase in sound intensity are represented by?
A rating system for the intensity of sound within the range of human hearing. A - a 10 unit change on the decibel scale. A sound 100x's more intense is rated 20 decibels higher and 1000x's more intense is 30 decibels higher.
Angle of incidence, angle of reflection, angle of refraction
Angle of refraction is smaller than incidence Angle of incidence equals angle of reflection
Explain why a pipe open at both ends gives all harmonics but a pipe open at one end and closed at the other gives only the odd harmonics. Use a diagram to illustrate your point.
For a pipe open at one end and closed at the other, the first harmonic features a node at one end and an antinode at the other. It is impossible to have a node at the open end of a pipe and impossible to have an antinode at the closed end of a pipe. (Speaking of displacement nodes/antinodes here, if you want to get technical.) These facts restrict the possible waveforms. The logical "next step," if you will, to move to the next harmonic from the first one is to add a node—this is impossible, however, because it would require that there be nodes at both ends of the pipe. Thus, we skip this step and add one node and one antinode to get the third harmonic. Notice that this follows the general pattern explained in the lessons that each successive harmonic will have one additional node and one additional antinode. In the case of resonators with mixed ends, however, the "next" harmonic will be the next odd harmonic—or the next possible harmonic given the limitations just described
Parallel light assumption
If object is far away from the lens it is assumed that the rays of light will hit the lens parallel, and the image will be at the focal point. As the object gets closer, the image will be below the focal point.
Infrasound is? Sound under what frequency?
Infrasound is sound of a frequency too low to be perceived by the human ear. Low frequency sound, under 20Hz which is the "normal" limit of human hearing.
Two lens system equations
Magnification = m1m2 Power = p1+p2 *Image formed by the first lens becomes the object for the second
Beat Frequency Does a standing wave transport any energy?
Occurs when two waves with close to the same frequency interfere. Fbeat= (F1-F2) - no NET transport, it does not propogate
Optical power formula
P = 1/f
What are photons, bending towards normal or away? How to visualize?
Physical "packets" (boxes) of light *when going into more dense, it goes towards normal *going into less dense, away from normal. The more dense pivots on the tire - much like what happens when a car tire goes off the road and hits a soft shoulder. What do you suppose will happen? Hopefully, it seems fairly intuitive that the "light packet" will tend to pivot around the corner that is "stuck" in the higher-index medium. Without plugging anything into Snell's Law, or memorizing a rule about which scenario causes light to bend "toward the normal vs. away from the normal," we can intuit exactly which way the light will bend.
Constructive interference
Regions where the amplitudes of superimposed waves add to each other, increasing amplitude.
Destructive interference
Regions where the amplitudes of superimposed waves subtract from each other, decreasing amplitude.
Draw a diagram of a ray of light being refracted at an interface where n1 < n2. Label the following: angle of incidence, angle of reflection, angle of refraction, n1, and n2. Describe the relationships between each value labeled on your drawing (i.e., are some values always equal, is one value usually larger than another, etc.)
See the diagram below: Ray P is an incident ray, Ray Q is a refracted ray, and Ray R is a reflected ray. The angle 1 is always exactly equal to the angle 3. The angles 1 and 2 are related to one another according to Snell's Law. Based on the direction of refraction alone, we know that n1 < n2. Because light waves travel faster in less dense mediums, we also know that v1 > v2. If we were to assume that the end of the blue shaded region represents the end of that medium, and that the white region below it represents a return to the same medium in which Rays P and R are traveling, then a continuation of Ray Q through this interface would create a newly refracted ray, Ray S. Ray S would be parallel to, but not continuous with, Ray P.
The Doppler effect formulas The greater the relative velocity the greater the shift in ?
Simplified formulas Δf/fs = v/c Δλ/λs = v/c frequency or wavelength.
Sound-proofing materials are used to isolate audiovisual production rooms and prevent the passage of sound into or out of the designated room. Rooms that are NOT constructed to such standards often allow the passage of sound through a wall because: A) sound waves can pass through microscopic pores in natural building materials. B) sound waves can pass through solid objects without losing amplitude or velocity. C) sound waves pass through solid objects, losing some amplitude, but maintaining a constant velocity D) sound waves pass through solid objects, exiting the solid with the same velocity they had just prior to striking the solid.
Sound waves can indeed pass through solids. In fact, they require a solid, liquid, or gas to act as the medium. Sound cannot travel in a vacuum. Answer A is false because sound waves pass through solids by vibrating through the solid itself, not by worming their way through tiny pores. Answer B is false because sound waves always lose some amplitude when passing through a solid due to reflection at the surface. Answer C is false because sound waves will increase speed when traveling through a more dense material. Answer D is correct. Recall that the medium determines the velocity. Assuming the air on either side of the object is equivlalent, the speed of the wave will also be the same on both sides.
Image types: Real
There is actual light at the image (image formed on your retina)
Transverse vs. longitudinal waves
Transverse waves displace the medium perpendicular to their direction of travel and longitudinal waves displace the medium parallel to their direction of travel (sound waves, p-wave earthquakes).
Convex mirrors
same as diverging lens
Ultrasound. Sound above what frequency?
Ultrasound is sound of a frequency too high to be perceived by the human ear. As an example, it is said that dogs can perceive ultrasonic sounds that humans cannot, and that elephants can perceive infrasonic sounds that humans cannot. High frequency sound, above 20,000 hertz. *Both use pressure waves
Wave Speed formula
V = fλ F=1/t
Units of Intensity
W/m2, watts per square metre, the power transferred per unit area
In order for two waves to have the same phase, what 3 things must be shared?
Wavelength, frequency, and period...NOT AMPLITUDE!
Energy of a photon formula? Many questions require you to combine the formula for the energy of a photon with the wave speed formula. Can you do this? What does it allow you to do?
You can combine the formula E = hf with the wave speed formula c = fλ (c = the speed of light) to obtain E = hc/λ. Since h and c are constants, this allows you to calculate the energy of a photon knowing only its wavelength. The MCAT has presented multiple problems that would require this approach.
If you forget which lens is which, you can always figure it out by employing the "packets of light" visualization. Recalling that light going through the lens will be slower than the light going through the air surrounding it, simply predict which way a light ray will bend near the top of the lens and near the bottom of the lens. This will reveal whether the lens diverges or converges light.
do it
Photoelectric effect is?
electrons are emitted from matter as a consequence of their absorption of energy from electromagnetic radiation of very short wavelength and high frequency, such as ultraviolet radiation.
Mirrors only equation
f=1/2r
What happens to period as harmonics increase?
gets shorter
It also helps to have had some recent real-life experience. Take out a spoon and look at the front and back. The front is a concave mirror and the back is a convex mirror.
haha
Image types: Virtual
no actual light emanating from or reaching the image (image formed behind the plane of the mirror)