Physics 170 - MechanicsLecture 34

Waves and sound II

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Sound WavesSound waves are pressure waves in solids, liquids, and gases. They are longitudinal in liquids and gases, and may have transverse components in solids.

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Compression

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Sound WavesThese pressure waves hit the eardrum and are converted to nerve impulses, which our brains interpret as sound.

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Sound WavesInfrasonic waves have frequencies too low for human ears. They are produced by earthquakes and other natural phenomena; elephants and cows can hear certain frequencies.Ultrasonic waves are too high in frequency for human ears. Dogs, cats, and bats can hear higher frequencies.7

Sound WavesUltrasound is used in nature by bats for echolocation; they can identify the location and speed of flying insects.

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Sound WavesUltrasound is also used commercially— in electric toothbrushes, jewelry cleaning, and many medical applications, both diagnostic and treatment.

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The Speed of Sound

Speed of sound in a solid:

Here, Y is Young’s modulus and ρ is the density. Speed of sound in a liquid:

B is the bulk modulus.

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Sound Intensity and Sound Intensity Level

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Sound intensity is measured on a logarithmic scale, in decibels:

Sound Intensity and Sound Intensity Level

Excessive sound intensities can permanently damage hearing — protect your ears!

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Example

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Note: Normal conversation’s intensity level is about 50 dB.

Sound Phenomena

• Reflection: the “bouncing” of sound waves off a surface

• Refraction: the “bending” of sound waves as they pass through a varying medium

• Diffraction: the “bending” of sound waves around an obstacle or opening

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Sound Phenomena

Sound refracts when the density of air changes.

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Sound Phenomena

Interference occurs when multiple waves propagate through the same medium. Interference may be either constructive or destructive.

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Sound PhenomenaWhether the interference is constructive or destructive depends on the phase and path length difference of the two waves.The relationship between the phase difference and the path length difference:

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Sound Phenomena

For constructive interference:

For destructive interference:

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Sound PhenomenaIf two sounds are very close in frequency, we perceive them as “beats”—variations in sound intensity.The beat frequency is the difference of the two frequencies:

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The Doppler EffectAs a car or train horn approaches you and then passes by, the pitch of the sound first rises and then falls.

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The Doppler EffectThe motion of the source causes the wavelength as received by the observer to be shorter when the source is approaching, resulting in a higher frequency.

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The Doppler EffectThe effect when the source is receding is the same except for the sign of its velocity. Combining both possibilities gives:

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Similarly, if the source is stationary and the observer is moving,

Example

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A student stands beside the tracks as a train rolls slowly past.He notes that the frequency of the train whistle is 442 Hz when the trainis approaching him and 441 Hz when the train is receding from him. Fromthis he can find the speed of the train. What value does he find?

The Doppler EffectIf an object is moving faster than the speed of sound, it will outpace its sound waves, creating a sonic boom. A similar phenomenon produces the wake from a boat—it is going faster than the wave speed in water.

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The Doppler Effect

The angle of the shock wave depends on the wave speed and the speed of the object.

M is called the Mach number.

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Summary

•The sound frequency spectrum is divided into infrasonic, audible, and ultrasonic frequencies.•The speed of sound depends on the elasticity and density of the medium; in general, sound travels faster in liquids than in gases, and faster in solids than in liquids.•The intensity varies inversely as the square of the distance from a point source.

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Summary•The sound intensity level scale is logarithmic, and is measured in decibels.•Sound wave interference from two point sources depends on phase and path length difference. Interference may be either constructive or destructive.•The Doppler effect is a shift in wavelength due to the motion of source, observer, or both.•An object traveling faster than the speed of sound in a medium will create a shock wave (sonic boom).

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