Sound

Consider a vibrating guitar string

String Vibrates

Piece of string undergoes harmonic motion

Air molecules alternatively compressed and rarefied

Producing a Sound Wave• Sound waves are longitudinal waves

traveling through a medium• A tuning fork can be used as an

example of producing 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

• 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

• 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

• Sound is really tiny fluctuations of air pressure• units of pressure: N/m2 or psi (lbs/square-inch)

• Carried through air at ~343 m/s (770 m.p.h) as compressions and rarefactions in air pressure

wavelengthcompressed gas

rarefied gas

• Wavelength () is measured from crest-to-crest• or trough-to-trough, or upswing to upswing, etc.

• For traveling waves (sound, light, water), there is a speed (c)

• Frequency (f) refers to how many cycles pass by per second• measured in Hertz, or Hz: cycles per second• associated with this is period: T = 1/f

• These three are closely related:f = v

or T

horizontal axis could be:space: representing snapshot in timetime: representing sequence at a par- ticular point in space

pres

sure

• Pitch refers to whether the sound is a high or low note (pitch -> frequency)

• 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

• Sound is a longitudinal wave, meaning that the motion of particles is along the direction of propagation

• Transverse waves—water waves, light—have things moving perpendicular to the direction of propagation

Waves in air can’t really be transverse, because the atoms/molecules are not bound to each other◦ can’t pull a (momentarily) neighboring molecule sideways◦ only if a “rubber band” connected the molecules would this

work◦ fancy way of saying this: gases can’t support shear loads

Air molecules can really only bump into one anotherImagine people in a crowded train station with hands in

pockets◦ pushing into crowd would send a wave of compression into

the crowd in the direction of push (longitudinal)◦ jerking people back and forth (sideways, over several

meters) would not propagate into the crowd◦ but if everyone held hands (bonds), this transverse motion

would propagate into crowd

Sound speed in air is related to the frantic motions of molecules as they jostle and collide◦ since air has a lot of empty space, the communication

that a wave is coming through has to be carried by the motion of particles

◦ for air, this motion is about 500 m/s, but only about 350 m/s directed in any particular direction

Solids have faster sound speeds because atoms are hooked up by “springs” (bonds)◦ don’t have to rely on atoms to traverse gap◦ spring compression can (and does) travel faster than

actual atom motion

Medium sound speed (m/s)

air (0C) 331

air (20C) 343

water 1497

gold 3240

brick 3650

wood 3800–4600

glass 5100

steel 5790

aluminum 6420

Speed of Sound in a Liquid• In a liquid, the speed depends on the

liquid’s compressibility and inertia

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

Bv

• 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

Yv

Medium Speed (m/s)

Air 343

Helium 972

Water 1500

Steel (solid)

5600

The speed of sound is higher in solids than in gases◦ The molecules in a

solid interact more strongly

The speed is slower in liquids than in solids◦ Liquids are more

compressible

propertyinertial

propertyelasticv

• 331 m/s is the speed of sound at 0° C• T is the absolute temperature

331273

m Tv

s K

• Mach Number = Object speed/ Speed of Sound

• Example: • The speed of sound in a

column of air is measured to be 356 m/s. What is the temperature of the air?

Intensity of Sound Waves• The average intensity of a wave is the

rate at which the energy flows through a unit area, A, oriented perpendicular to the direction of travel of the wave

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

1 EI

A t A

• 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

• The sensation of loudness is logarithmic in the human hear

• β is the intensity level or the decibel level of the sound

• Io is the threshold of hearing10 log

o

II

• 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

• Some examples (1 pascal 10-5 atm) :

Sound Intensity Pressure Intensityamplitude (Pa) (W/m2)

level (dB)Hearing threshold 3 10-5 10-12

0Classroom 0.01 10-7 50City street 0.3 10-4 80Car without muffler 3 10-2 100Indoor concert 30 1 120Jet engine at 30 m. 100 10 130

• Example: • A family ice show is held at an enclosed area.

The skaters perform to music playing at a level of 80.0 dB. The intensity level of music playing is too loud for your baby brother who yells at 75.0 dB. (a) What total sound intensity is produced? (b) What is the combined sound level?

• 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

• Assumptions:• The air is stationary• All speed measurements are made relative to the

stationary medium

• An observer is moving toward a stationary source

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

• The frequency heard is increased

• An observer is moving away from a stationary source

• The observer detects fewer wave fronts per second

• The frequency appears lower

• 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

• 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

• 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

• 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

ƒ ƒ oo s

s

v vv v

• Example:• As a truck travelling at 96 km/hr approaches and

passes a person standing along the highway, the driver sounds the horn. If the horn has a frequency of 400 Hz, what are the frequencies of the sound waves heard by the person

• (a) as the truck approaches?• (b) after it has passed?