Unit 10: Part 2Sound

outline

Sound Waves

The Speed of Sound

Sound Intensity and Sound Intensity Level

Sound Phenomena

The Doppler Effect

Musical Instruments and Sound Characteristics

Sound Waves

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

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

Sound Waves

Infrasonic 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.

Sound Waves

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

Sound Waves

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

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.

The Speed of Sound

Speed of sound in dry air:

Note the dependence on temperature.

Sound Intensity and Sound Intensity Level

Intensity is the power per unit area; it is inversely proportional to the square of the distance from a point source.

Sound Intensity and Sound Intensity Level

We perceive sound intensity as loudness; the minimum detectable sound has an intensity of about 1.0 × 10–12 W/m2, and the threshold of pain occurs at an intensity of about 1.0 W/m2.

A doubling of loudness corresponds to an increase in intensity of about a factor of 10.

Sound Intensity and Sound Intensity Level

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

Sound Intensity and Sound Intensity Level

Sound Intensity and Sound Intensity Level

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

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

Sound Phenomena

Sound refracts when the density of air changes.

Sound Phenomena

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

Sound Phenomena

Whether 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:

Sound Phenomena

For constructive interference:

For destructive interference:

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:

The Doppler Effect

As a car or train horn approaches you and then passes by, the pitch of the sound first rises and then falls. This is called the Doppler effect.

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.

The Doppler Effect

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

The Doppler Effect

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

The Doppler effect occurs with electromagnetic waves as well; this is how a radar gun works.

The Doppler Effect

If 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.

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

M is called the Mach number.

Musical Instruments and Sound Characteristics

Many musical instruments produce sound via standing waves, in one way or another. Strings support standing waves; the length of the string can be varied on some instruments such as violins and guitars.

Piano strings are fixed-length; their density varies from one note to the next, keeping the length difference from lowest to highest to a minimum.

Musical Instruments and Sound Characteristics

Standing waves can also exist in tubes or pipes, such as woodwind and brass instruments. Organ pipes are fixed in length; there is one (or more) for each key on the keyboard.

Musical Instruments and Sound Characteristics

The pitch of woodwind instruments can be varied by covering and uncovering holes in the tube.

Musical Instruments and Sound Characteristics

The sensitivity of the human ear to sound varies with frequency. Sounds of the same intensity at different frequencies will not sound equally loud.

Musical Instruments and Sound Characteristics

In general, the way we perceive sound is related to its physical properties, but depends on other factors as well.

Musical Instruments and Sound Characteristics

The quality of a sound—that which distinguishes a violin from a bagpipe from a human voice—depends on the shape of its waveform. The fundamental frequency, which we perceive as the pitch, is enhanced by overtones, giving the sound its characteristic quality.

Musical Instruments and Sound Characteristics

The sum of the fundamental frequency and the overtones gives the final waveform.

SummaryThe 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.

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.

Summary

An object traveling faster than the speed of sound in a medium will create a shock wave (sonic boom).

Standing waves may be formed inside both closed and open pipes.