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/m 2 or psi (lbs/square-inch) Carried through air at ~343 m/s (770 m.p.h) as compressions and rarefactions in air pressure wavelength compressed 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 time time: representing sequence at a par- ticular point in space pressure

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 another Imagine 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

Mediumsound speed (m/s) air (0  C) 331 air (20  C) 343 water1497 gold3240 brick3650 wood3800–4600 glass5100 steel5790 aluminum6420

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

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

MediumSpeed (m/s) Air343 Helium972 Water1500 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

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

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/m 2

Threshold of hearing Faintest sound most humans can hear About 1 x W/m 2 Threshold of pain Loudest sound most humans can tolerate About 1 W/m 2 The ear is a very sensitive detector of sound waves It can detect pressure fluctuations as small as about 3 parts in 10 10

The sensation of loudness is logarithmic in the human hear β is the intensity level or the decibel level of the sound I o is the threshold of hearing

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  atm) : Sound IntensityPressureIntensity amplitude (Pa)(W/m 2 )level (dB) Hearing threshold3  Classroom City street Car without muffler Indoor concert Jet engine at 30 m

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 –v o for v o in the above equation

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 –v s when the source is moving toward the observer and +v s when the source is moving away from the observer

Both the source and the observer could be moving Use positive values of v o and v s if the motion is toward Frequency appears higher Use negative values of v o and v s if the motion is away Frequency appears lower

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?