Music

Physics 202Professor Lee

CarknerLecture 9

PAL #9 Sound Interference from two loudspeakers

To get destructive interference you want the received waves to be out of phase by ½ wavelength

f = 1150 Hz, v = 343 m/s (for room temperature

air) v = f, = v/f = 343/1150 = 0.3 m If L1 is 4m, make L2 4.15 m

L2 = 4 m (or 4.3 m or 3.7 m etc.)

Music We shall consider an generalized

instrument consisting of a pipe which may be open at one or both ends

There will always be a node at the closed end and an anti-node at the open end

Harmonics

For resonance need a integer number of ½ wavelengths to fit in the pipe

L = ½ n v = ff = nv/2L

n = 1,2,3,4 …

For resonance need an integer number of

¼ wavelengths to fit in the pipe

L = ¼ n v = ff = nv/4L

n = 1,3,5,7 … (only have odd harmonics)

The Decibel Scale

To model ear’s logarithmic response, we use the decibel scale

= (10 dB) log (I/I0) I0 = 10-12 W/m2 (at the threshold of human

hearing)

10 times louder means 10 dB greater level

Sound Levels

A pain level sound is a trillion times as intense as a sound you can barely hear

Your hearing response is logarithmic A sound 10 times as

intense sounds twice as loud

Hearing Threshold

Whisper

Talking

Rock Concert

Pain 120 dB

The Doppler Effect

If there is any relative motion between the two, the frequency of sound detected will differ from the frequency of sound emitted

Frequency Change If the source and the detector are moving

closer together the frequency increases

If the source and the detector are moving further apart the frequency decreases

General Doppler Effect

f’ = f ( v±vD / v±vS ) What sign should be used?

Do this twice to find the numerator and denominator sign For motion toward, the sign should be chosen to

increase f’

Remember that the speed of sound (v) will often be 343 m/s

Next Time

Read: 18.1-18.6

Consider a sound wave with a fixed amplitude and frequency. How would you change the properties of the medium through which it passes to maximize its

speed? a) Increase , increase Bb) Increase , decrease Bc) Decrease , increase Bd) Decrease , decrease Be) Speed will only change if we

change the frequency

Consider a sound wave with a fixed amplitude and frequency. How would you change the properties of the medium to

maximize its pressure amplitude?

a) Increase , increase Bb) Increase , decrease Bc) Decrease , increase Bd) Decrease , decrease Be) Speed will only change if we

change the frequency

If you were producing the sound with a speaker, as you changed the medium toincrease the pressure amplitude, does driving the speaker become harder, easier or stay the same?

a) Harderb) Easierc) Stay the same

If the density of air doubles (with no other changes) what happens to the intensity of

sound in that air?

a) Decreases by square root of 2b) Decreases by factor of 2c) Stays the samed) Doublese) Increases by square root of 2

Consider two sound detectors. Detector A is 1 meter away from a sound source and detector B is 3 meters away. If each detector receives the same amount of energy per second, what is the ratio of the areas of the detectors (area A/area B)?a) 1/9b) 1/3c) 1d) 3e) 9

Summary: Sound Waves

Sound waves are longitudinal or pressure waves

The medium oscillates in the direction of travel

The speed of sound depends on the density and the bulk modulus (compressibility ) of the medium:

v = (B/)½

Summary: Wave Equations

The equations for the amplitude and pressure of a sound wave are:

s = sm cos (kx-t)

p = pm sin (kx-t)

pm = (v) sm

Waves from two sources will interfere based on the path length difference between the sources and detector

L = m (fully constructive)L = (m+½) (fully destructive)

Summary: Intensity and Music The intensity of sound falls off with a inverse

square law:I = Ps/4r2

I =½v2sm2

The sound level is: = (10 dB) log (I0/I)

Harmonic frequencies of a pipef = nv/2L (open at 2 ends)f = nv/4L (open at 1 end)

Beat frequency = fbeat = f1 - f2

Summary: Doppler Effect Relative motion together produces

an increase in frequency Relative motion apart produces a

decrease in frequencyf’ = f ( v±vD / v±vS )