Chapter 15

Sound

Producing a Sound Wave• All sound waves begin in a vibrating object.

• Source vibrates at an audible frequency.• Sound waves are longitudinal waves traveling through a

medium.• Elements of a medium are displaced in a direction parallel to

the direction of wave motion.• A tuning fork can be used as an example of an object

producing a sound wave.

Using a Tuning Fork to Produce a Sound Wave

• A tuning fork will produce a pure musical note.

• As the tines vibrate, they disturb the air near them.

• As the tine swings to the right, it forces the air molecules near it closer together.

• This produces a high density area in the air.• This is an area of compression.

Using a Tuning Fork

• As the tine moves toward the left, the air molecules to the right of the tine spread out.

• This produces an area of low density.• This area is called a

rarefaction.

Using a Tuning Fork

• As the tuning fork continues to vibrate, a succession of compressions and rarefactions spread out from the fork.

• A sinusoidal curve can be used to represent the longitudinal wave.• Crests correspond to compressions and troughs to rarefactions.

rarefactions

compression

Categories of Sound Waves

• Audible waves• Lay within the normal range of hearing of the human ear.• Normally between 20 Hz to 20,000 Hz.

• Infrasonic waves• Frequencies are below the audible range.• Earthquakes are an example.

• Ultrasonic waves• Frequencies are above the audible range.• Dog whistles are an example.• These sound waves are generated using the piezoelectric

effect.

Generating Ultrasonic Waves

• Demonstrates the piezoelectric effect.• Electricity provides the mechanical energy to vibrate the crystal at

certain frequency.

Speed of Sound in Air

• In air, the speed of sound depends on the wavelength, the frequency, and the temperature:

• Remember this equation from chapter 14.• The speed of sound increases by about 0.6 m/s for each 1oC

increase in the temperature of the air.

v = ƒλ

Speed of Sound in Air

• The speed of sound in a medium also depends upon the temperature.

• For sound in air:

• 331 m/s is the speed of sound at 0° C (273 K).• T is the absolute temperature.

331273

m Tv

s K

Sample Problem

Find the wavelength in air at 20o C of an 18 Hz sound wave, which is one of the lowest frequency that is detectable by the human ear.

Speed of Sound in a Fluid• In a liquid, the speed depends on the fluid’s compressibility

and inertia:

• B is the Bulk Modulus of the fluid.• ρ is the density of the fluid.• Compares with the equation for a transverse wave on a string:

Bv

Speed of Sound in a Solid

• The speed depends on the rod’s compressibility and inertial properties:

• Y is the Young’s Modulus of the material.• ρ is the density of the material.• Speed of sound in solids greater than speed of sound in fluids.

Yv

Typical Values for Elastic Moduli

Comparison of Speed of Sound in Various Mediums

• Speed of sound in gases and liquids are more temperature dependent than the speed of sound in solids.

• Thus there is a dependence upon the temperature of the medium.

Intensity of Sound Waves

• The average intensity (I ) of a wave on a given surface is defined as the rate at which the energy flows through the surface divided by the surface area, A:

• The direction of energy flow is perpendicular to the surface at every point.• The area is perpendicular to the direction of energy flow.

• The rate of energy transfer is the power.• Units are W/m2.

1 EI

A t A

The Ear• The ear serves as an “area”

that “concentrates” the sound and increases the intensity of sound.

• Threshold of hearing:• Faintest sound most humans

can hear• About 1 x 10-12 W/m2

• Threshold of pain:• Loudest sound most humans

can tolerate• About 1 W/m2

• The ear is a very sensitive detector of sound waves.• It can detect pressure

fluctuations as small as about 3 parts in 1010.

Intensity Level of Sound Waves

• The human ear’s sensation of loudness is not a direct linear relationship to the intensity of the sound.• The sensation of loudness is logarithmic in the human hear.

• β is the intensity level or the decibel level of the sound.• This is the relative loudness of the sound.• Can be calculated using:

• Io is the threshold of hearing ( = 10-12 W/m2)

10 log

o

II

Various Intensity Levels

• Threshold of hearing is 0 dB.• Threshold of pain is 120 dB.• Jet airplanes are about 150

dB.• Table 14.2 lists intensity

levels of various sounds.• Multiplying a given intensity

by 10 adds 10 dB to the intensity level.

Frequency Response Curves

• Bottom curve is the threshold of hearing.• Threshold of hearing

is strongly dependent on frequency.

• Easiest frequency to hear is about 3300 Hz.

• When the sound is loud (top curve, threshold of pain) all frequencies can be heard equally well.

Doppler Effect

• A Doppler effect is experienced whenever there is relative motion between a source of waves and an observer.• When the source and the observer are moving toward each other,

the observer hears a higher frequency.• When the source and the observer are moving away from each

other, the observer hears a lower frequency.• Although the Doppler Effect is commonly experienced with

sound waves, it is a phenomena common to all waves.• We will examine three cases:

• Case 1: A stationary source & moving observer• Case 2: A moving source & stationary observer• Case 3: Moving source & moving observer

Frequency of Sound: Two Stationary Objects

• Wave fronts have a certain wavelength and thus will have a certain frequency as well.

• A stationary observer to the right of the wave front will experience the same frequency as emitted by the source, with no change to the observed frequency.• fsource = fobserved

• When either the object or source moves the observed frequency changes.• This produces the Doppler effect.

Doppler Effect Case 1: (A stationary source & moving observer)

• An observer is moving toward a stationary source.

• Due to his movement, the observer detects an additional number of wave fronts.• Thus the velocity of the

observer will factor into the frequency observed.

• The frequency heard is increased.

Doppler Effect Case 1: Equation

• When moving toward the stationary source, the observed frequency is:

• When moving away from the stationary source, substitute –vo for vo in the above equation.

ƒ ƒ oo s

v vv

+Vo

-Vo

Doppler Effect Case 2: (A moving source & stationary observer)

• The observed frequency will depend on the velocity of the source and the position of the observer

• As the source moves toward the observer (A), the wavelength appears shorter and the frequency increases.

• As the source moves away from the observer (B), the wavelength appears longer and the frequency appears to be lower.

Doppler Effect Case 2: Equation

• Use the –vs when the source is moving toward the observer and +vs when the source is moving away from the observer.

ƒ ƒo ss

vv v

Doppler Effect Case 3 (Moving source & moving observer)

• Both the source and the observer could be moving:

• Use positive values of vo and vs if the motion is toward.• Frequency appears higher.

• Use negative values of vo and vs if the motion is away.• Frequency appears lower.

Sample Problem

A trumpet player sounds C above middle C (524 Hz) while traveling in a convertible at 24.6 m/s. If the car is coming toward you, what frequency would you hear? Assume the temperature is 20o C.

Standing Waves

• When a traveling wave reflects back on itself, it creates traveling waves in both directions.

• The wave and its reflection interfere according to the superposition principle.

• With exactly the right frequency, the wave will appear to stand still.• This is called a standing

wave.

Characteristics of Standing Waves

• Different frequencies will yield different standing waves.

• The more loops the higher the frequency.

• The wavelength and frequency for each type of standing wave can be calculated.

• The frequency used to generate the wave with only one antinode is as the fundamental frequency.

Standing Waves on a String

• Standing waves can very easily be generated on a string or rope.• A simple change in the frequency of vibration will alter the type of

standing wave we get.• Nodes must occur at the ends of the string because these

points are fixed.

Allowed and Forbidden Frequencies

• The allowed standing waves correspond to whole number integers of the fundamental frequency.

• We can calculate for the frequency of the nth harmonic using:

1ƒ ƒ2n

n Fn

L

Standing Waves in Air Columns

• When we blow across a pipe we create standing longitudinal waves, similar to the standing transverse waves generated in the string.

• Characteristics of these standing waves are similar to the standing transverse waves.

Tube Open at Both Ends

• If the end is open, the elements of the air have complete freedom of movement and an antinode exists.

Frequencies in Air Column Open at Both Ends

• In a pipe open at both ends, the natural frequency of vibration forms a series whose harmonics are equal to integral multiples of the fundamental frequency:

• This is almost exactly the same as the standing transverse wave.• The velocity is the velocity of sound in air.

• All harmonics are present.

1ƒ ƒ 1, 2, 3,2n

vn n n

L

Tube Closed at One End

• If one end of the air column is closed, a node must exist at this end since the movement of the air is restricted.

Frequencies in an Air Column Closed at One End

• The closed end must be a node.• The open end is an antinode.• There are no even multiples of the fundamental harmonic:

• Thus not all harmonics are present.

1ƒ 1, 3, 5,4n

vf n n n

L

Sample Problem

When a tuning fork with a frequency of 392 Hz is used with a closed-pipe resonator, the loudest sound is heard when the column is 21.0 cm and 65.3 cm long. What is the speed of sound in this case?

Chapter 15

Sound

THE END