Kaplan MCAT Physics Chapter 7: Waves and Sound 7%

frequency of the vibration of a string

= srt (T/p / lambda) where f is frequency, T is tension in the string, p is the linear density (mass per unit of length), and lambda is equal to the wavelength.

ULTRA SOUND USES TRAVEL TIME OF ______________TO CALCULATE DISTANCE

THE REFLECTED SOUND

Wavelength

The distance between two crest and two troughs

In reality, there are resistive forces (i.e. nonconservative forces) which act in opposite directions which

decrease the amplitude of the wave. IT DOES NOT DECREASE FREQUENCY.

phase difference

is the extent to which the waves are offset. The higher the phase difference, the more offset the wave.

trough

lowest point wave reaches

unit of wavelength

meters

Wavelength and Frequency of a standing wave (strings and open pipes)

n = nonzero integer called a harmonic. A harmonic corresponds to the number of half-wavelengths supported by a string.

light waves are______and sound waves are _______

transverse, longitudinal

velocity of a wave

v = fλ

What is a closed boundary open boundary?

A closed boundary is a boundary that does not allow oscillation, and therefore corresponds to a node. A string tied to a brick wall would be a good example of a closed boundary. Also the closed end of a pipe antinodes

Doppler effect

A shift in the perceived frequency of a sound compared to the actual frequency of the emitted sound when a source of the sound and the detector are moving relative to one another.

Sound Level

B = sound level (measured in decibels) I = intensity of wave Io = threshold of hearing threshold of hearing 1*10-12 W/m2

Closed pipes

Also support standing waves, and the length of the pipe is equal to some odd multiple of quarter-wavelength.

Angular frequency

Another way of representing frequency expressed in radians per second.

supersonic speed

Any speed that is faster than the speed of sound in the substance of interest When the speed of the source > speed of sound → waves constructively interfere and result in increased amplitude known as a shock wave → shock waves result in high pressure followed by low pressure → this results in a sonic boom.

Change in Sound Level

B = sound level (measured in decibels) I = intensity

What is bulk modulus?

Bulk modulus is a measure of an object's resistance to compression. Bulk modulus is lowest in gases (easily compressed) and highest in liquids and solids (almost impossible to compress)

How does one determine the harmonic of a standing wave in a closed pipe?

Count the number of quarter wavelengths.

Dampening, Attenuation

Decrease in amplitude of waves caused by an applied or nonconservative force

Longitudinal waves

Have oscillations of wave particles parallel to the direction of wave propagation (example: sound waves)

Transverse waves

Have oscillations of wave particles perpendicular to the direction of the wave propagations.

Displacement (x)

In a wave, displacement refers to how far a point is from the equilibrium position, expressed as a vector quantity.

overtone

In an object that produces multiple frequency waves when struck, the overtones are the higher frequency waves.

Infra/Ultrasonic

Infra<20Hz Ultra>20,000Hz

How is the amplitude of a sound wave related to its intensity? distance?

Intensity increases proportional to the square of the amplitude. This means that, if you double the amplitude, you will quadruple the intensity. Intensity of sound is inversely proportional to the square of the distance. This means that if you are twice as far away from a sound, it will be 1/4 times as intense. If you are 3 times as far away from a sound, it will be 1/9 times as intense.

Sound

Longitudinal waves transmitted by the oscillation of particals in a deformable medium. B-bulk modulus

Antinodes

Midway between nodes, max amplitude

Partial constructive / destructive interference

Occurs when two waves are not quite perfectly in or out of phase with each other. Sum of waves nearly in phase

Constructive interference

Occurs when waves are exactly in phase with each other. The amplitude of the resultant wave is equal to the sum of the amplitudes of the two interfering waves.

Destructive interference

Occurs when waves are exactly out of phase with each other. The amplitude of the resultant wave is equal to the difference in amplitude between the two interfering waves. 180 degrees out of phase

Nodes

Points of waves that remain at rest, amplitude=0 Nodes are the point of NO D(E)isplacement

Noise

sounds not particularly musical, have multiple frequencies at once

Standing waves

Produced by constructive and destructive interference of two waves at same freq traveling in opposite directions in same space. Both ends of string fixed. Interference between traveling and reflected wave make it appear stationary.

Timbre

Quality of sound. One natural frequency sounds more pure than multiple.

Sound speed

Sound propagates through all forms of mater: 1) Fastest through solids with low density, followed by liquids, and slowed through very dense gases. 2) Within a medium, as the density increases, the speed of the sound decreases. B = bulk modulus p = density

What makes music sound like music and not like noise?

The fact that the multiple frequencies at which the object vibrates are related to eachother by whole number ratios instead of just being randomly related.

Amplitude (A)

The magnitude of its maximal displacement.

Crest

The maximum point of a wave (point of most positive displacement)

Frequency

The number of cycles a wavelength makes per second. Expressed in hertz (Hz) 1Hz= 1/s

Period (T)

The number of seconds it takes to complete a cycle. It is the inverse of frequency. T = 1/f

First, Second, and Third Harmonics of an Closed Pipe

The second overtone is the third harmonic, given by n=3 for open systems and 5th harmonic, given by n=5 for closed systems

Pitch

The sound as related to its frequency. High pitch = high frequency Low pitch = low frequency

Doppler effect equation

Top sign = "toward" Bottom sign = "Away" vd is speed of detector vs is speed of source v = speed of sound = 340 m/s vs>vd then fprime>f

Traveling wave

Wave moves. Reaches fixed boundary and is reflected and inverted hit fixed boundary cause incident wave to be reflecgted and undergo 180 phase change

Loudness/Volume

Way we percieve its intentsity

Ultrasound waves

When the sound waves travel through the body, they encounter various tissues. Whenever a sound wave passes into a new tissue, some of the wave passes through the tissue and some is reflected back to the source. Different tissues allow different amounts of wave to reflect back to the source. The more the tissue reflects back to the source, the more brightly the tissue will appear on ultrasound.

Intensity Equation

average rate of E transfer per A across surface perp to wave (W/m^2) Intensity of sound is the average rate of energy transfer per area a sound wave makes on a surface.

Open Pipe

both ends Support standing waves

Resonating

frequency of periodic force is equal to natural freq of system

When the source and detector are moving toward eachother, the perceived frequency is

greater

Resonance

increase in amplitude that occurs when a periodic force is applied at the natural (resonant) frequency of an object Any solid object, when hit, struck, rubbed, or disturbed physically in any way, will begin to vibrate.

First, Second, and Third Harmonics of a String

number of antinodes = which harmonic

First, Second, and Third Harmonics of an Open Pipe

number of nodes = which harmonic

Closed Boundaries

one end support standing waves

Forced Oscillation

periodically varying force applied to a system, system driven at frequency equal to frequency of F.

equilibrium position

the central point around which a wave oscillates

wavlength

the distance between successive crests of a wave, especially points in a sound wave or electromagnetic wave.

For a given medium → the higher the temperature →

the more oscillations can take place → the faster the speed of sound in that medium

When the speed of the source = speed of sound

the wave fronts pile up directly in front of the source.

Principle of superposition

when waves interact with each other, the displacement of the resultant wave at any point is the sum of the displacements of the two interacting waves

A transducer sends out high frequency pulses of sound (aka low wavelength), the sound wave is then reflected and the transducer detects this.

■ how long that sound wave took to be reflected. ■ It repeats this process over and over and over again against a bunch of different interfaces in the medium of question to generate an image. ■ Note the high frequency is needed in order to minimize diffraction (since wavelength is very small).

Doppler ultrasound

○ Doppler ultrasound → this uses the fact that blood moving will generate a doppler effect → as such, it detects the frequency shift to determine the flow of blood within the body.