Week 5: Traveling Waves and Sound

circular waves

A circular wave is a two dimensional wave that spreads across a surface. • In a photograph of ripples in a pond, the locations of the crests would be the wave fronts. They are spaced one wavelength apart • Although the wave fronts are circles, the curvature isn't noticeable if you observed a small section of the wave front very far away from the source.

disturbance

A disturbance is a wave that passes through a medium, displacing the atoms that make up the medium from their equilibrium position. • A wave disturbance is created by a source. • Once created, the disturbance travels outward through the medium at the wave speed

plane waves

A plane wave describes observations of waves far from their source. The planes represent the crests of the spherical waves

shock wave

A shock wave is produced when a source moves faster than the waves, which causes waves to overlap. • The overlapping waves add up to a large amplitude wave, which is the shock wave. A source is supersonic if it travels faster than the speed of sound. • A shock wave travels with the source. If a supersonic source passes an observer, the shock wave produces a sonic boom. • Less extreme examples of shock waves include the wake of a boat and the crack of a whip

math description of sin waves

A sinusoidal wave is the type of wave produced by a source that oscillates with simple harmonic motion (SHM). • The amplitude A is the maximum value of displacement. • The crests have displacement of A and the troughs have a displacement of −A. The wave, like SHM, is repetitive. • The wavelength l is the distance spanned in one cycle of the motion.

Snapshot and History Graphs

A snapshot graph shows a wave's displacement as a function of position at a single instant of time As the wave moves, we can plot a sequence of snapshot graphs like successive frames from a video. • These graphs show the motion of the wave, but that's only half the story. • Now we want to consider the motion of the medium. • In each of the graphs we've placed a dot, located at position x1, at one point on the string. • We use the vertical positions to show the motion of one point on the string.

Sound Waves from a Moving Source

A source of sound waves is moving away from Pablo and towards Nancy with a speed vs. • The subscript on vs means it is the velocity of the source, not the speed of the waves. • The source emits a frequency fs as it travels. • After a wave crest leaves the source, its motion is governed by the properties of the medium. The motion of the source has no affect on each crest once emitted. Each circular wave front is centered on where it was emitted. • Due to the motion of the source, the wave crests bunch up in the direction of motion of the source, and are stretched behind it The wavelength is the distance between crests. • Nancy measures a wavelength that is less than if the source were stationary l = 0 s v f / where v is the velocity of the wave and l0 is the wavelength observed by Nancy. • Similarly, the wavelength is larger behind the source The frequency l + + f v = / detected by the observer whom the source is approaching is higher than the frequency emitted by the source. The observer behind the source detects a lower frequency f− than the source emits

Waves on a String

A transverse wave pulse traveling along a stretched string is shown below. • The curvature of the string due to the wave leads to a net force that pulls a small segment of the string upward or downward. Each point on the string moves perpendicular to the motion of the wave, so a wave on a string is a transverse wave. • An external force created the pulse, but once started, the pulse continues to move because of the internal dynamics of the medium.

traveling wave

A traveling wave is an organized disturbance that travels with a well-defined wave speed.

Energy and Intensity

A traveling wave transfers energy from one point to another. • The power of the wave is the rate at which the wave transfers energy and is measured in watts. • To understand how to characterize the power of waves, we must first understand how waves change as they spread out.

traveling waves

A wave is not a particle, so we cannot use Newton's laws on the wave itself. • The medium is made of particles, so we can use Newton's laws to examine how the medium responds to a disturbance

Frequency Shift on Reflection from a Moving Object

A wave striking a barrier or obstacle can reflect and travel back to the source. For sound, this is an echo. • For an object moving toward a source, it will detect a frequency Doppler shifted to a higher frequency. • The time between the emission of a pulse and its return gives an object's position. • The change in frequency of the returned pulse gives the object's speed.

Light and Other Electromagnetic Waves

An electromagnetic wave is the oscillation of the electromagnetic field. • Electromagnetic waves include visible light, radio waves, microwaves, and ultraviolet light. Electromagnetic waves have extremely short wavelengths. In air, visible light has a wavelength of roughly 400-700 nm. • Each wavelength is perceived as a different color. Longer wavelengths (600-700 nm) are seen as orange and red light while shorter wavelengths (400-500 nm) are seen as violet and blue light. The visible spectrum is a small slice out of the much broader electromagnetic spectrum.

Sound Waves

As the cone of a loudspeaker moves forward, it moves air molecules closer together, creating a region of higher pressure. A half cycle later, the cone moves backward, and pressure decreases. • The regions of higher and lower pressures are called compressions and rarefactions, respectively. The pressure waves of sound oscillate sinusoidally around the atmospheric pressure patmos. • When the wave reaches your ear, the oscillating pressure causes your eardrum to vibrate and then transferred to the cochlea, where it is sensed. • Humans with normal hearing can detect a range of 20 Hz to 20,000 Hz

Electromagnetic and Matter Waves

Electromagnetic waves are waves of an electromagnetic field. They include visible light, radio waves, microwaves, and x rays. • Electromagnetic waves require no material medium and can travel through a vacuum. • Matter waves describe the wave-like characteristics of material particles such as electrons and atoms at an atomic scale.

speed of light

Electromagnetic waves, such as light, travel at much higher speeds than mechanical waves. • The speed of light c is the speed that all electromagnetic waves travel in a vacuum. • The value of the speed of light is 3.00 x10 ^8m/s •Although light travels more slowly in air than in a vacuum, this value is still a good approximation for the speed of electromagnetic waves through air. • At this speed, light could circle the earth 7.5 times in 1 s

Transverse waves

For mechanical waves, a transverse wave is a wave in which the particles in the medium move perpendicular to the direction in which the wave travels. Shaking the end of a stretched string up and down creates a wave that travels along the string in a horizontal direction while the particles that make up the string oscillate vertically

Loudness of Sound

Generally, increasing the sound intensity by a factor of 10 results in an increase in perceived loudness by a factor of approximately 2. • The loudness of sound is measured by a quantity called the sound intensity level. • The sound intensity level is measured on a logarithmic scale because the perceived loudness is much less than the actual increase in intensity.

The Doppler Effect for Light Waves

If the source of light is receding from you, the wavelength you detect is longer than that emitted by the source. The light is shifted toward the red end of the visible spectrum; this effect is called the red shift. • The light you detect from a source moving toward you is blue shifted to shorter wavelengths. All distant galaxies are red shifted, so all galaxies are moving away from us. Extrapolating backward brings us to a time where all matter in the universe began rushing out of a primordial fireball in an event known as the Big Bang. • Measurements show the universe began 14 billion years ago

longitudinal wave

In a longitudinal wave, the particles in the medium move parallel to the direction in which the wave travels. Quickly moving the end of a spring back and forth sends a wave—in the form of a compressed region—down the spring. The particles that make up the spring oscillate horizontally as the wave passes.

mechanical waves

Mechanical waves are waves that involve the motion of the substance through which they move. The substance is the medium. A wave does transfer energy, but the medium as a whole does not travel. • A wave transfers energy, but it does not transfer any material or substance outward from the source

sound

Sound speed is slightly less than the rms speed of the molecules of the gas medium, though it does have the same dependence on temperature and molecular mass: = 343 m/s At a given temperature, the speed of sound increases as the molecular mass of the gas decreases. Thus the speed of sound in room-temperature helium is faster than that in room temperature air. • The speed of sound doesn't depend on the pressure or the density of the gas. • The speed of sound in liquids is faster than in gases, and faster in solids than in liquids.

spherical waves

Spherical waves move in three dimensions. Light and sound waves are spherical waves. • The waves are three-dimensional ripples; the crests are spherical shells still spaced one wavelength apart. • The wave-front diagrams are now circles that represent slices through the spherical shells locating the wave crests. When you observe a wave far from its source, the small piece of the wave front is a little patch of the large sphere. The curvature of the sphere will be unnoticed, and the wave front will appear to be a plane.

intensity

The intensity of light or sound (brightness or loudness) depends on the power of the source and the area that receives the power: I = P/a The SI units are W/m^2• A wave focused on a small area has higher intensity than if it were spread out If a source of spherical waves radiates uniformly in all directions, then the surface area of the sphere is 2 4pr and the intensity is: I = P/4pir^2

period and frequency on SHM

The period T of the wave is the time interval to complete one cycle of motion. • The wave frequency is related to the period T f = 1/ , exactly the same as in SHM. Therefore the motion of the point is y(t) = Acos(2pi(t/T))

Decibel scale

The threshold of hearing is the lowest intensity sound that can be heard. It is where we place the 0 for our loudness scale for avg human it is I = 10^-12 sound intensity level beta = 10log10(I/I0) in dB

earthquake waves

The two most important types of earthquake waves are S waves (transverse) and P waves (longitudinal). • The P waves are faster, but the S waves are more destructive.

Wave Speed Is a Property of the Medium

The wave speed does not depend on the size and shape of the pulse, how the pulse was generated or how far it has traveled—only the medium that carries the wave. • Strings - properties that determine speed are string's mass, length, and tension. A string with a greater tension responds more rapidly, so the wave will move at a higher speed. Wave speed increases with increasing tension. • A string with a greater linear density has more inertia. It will respond less rapidly, so the wave will move at a lower speed. Wave speed decreases with increasing linear density vstring = sqrt(Ts/u)

ultrasound waves

Ultrasound waves are high-frequency sounds above our range of hearing that are used by some animals for echolocation. • The resolution that can be detected by an optical instrument or your eyes is limited by the wavelength of the light. Acoustic imaging is the same; the higher the frequency (thus the shorter the wavelength), the finer the detail. • Animals that use echolocation, such as bats and porpoises, produce and sense high-frequency sounds

linear density

u = m/L characterizes the type of string we are using

The Fundamental Relationship for Sinusoidal Waves

v = gamma/T

The Doppler Effect and Shock Waves•

v• The Doppler effect is a change in frequency due to the motion of the source or observers. • This effect is heard as the higher pitch of an ambulance siren as it approaches you and drops after it has passed you by. • A shock wave is produced when an object moves faster than the speed of sound. • When you hear the crack of the whip, the tip of a whip is moving at supersonic speeds The Doppler effect is the change in frequency when a source moves relative to an observer.

displacement as a funciton of distance

y(x) = Acos(2pi (x/gamma))

displacement of a traveling wave

y(x,t) = Acos(2pi((x/gamma) - t/T)) - is to move right + is to move left

the wave model

• The wave model describes the basic properties of waves and emphasizes those aspects of wave behavior common to all waves.