Music Physics 202 Professor Lee Carkner Lecture 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 L 1 is 4m, make L m   L 2 = 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 = f f = 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 = f f = 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/I 0 )   I 0 = W/m 2 (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±v D / v±v S )  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:

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 B b)Increase , decrease B c)Decrease , increase B d)Decrease , decrease B e)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 B b)Increase , decrease B c)Decrease , increase B d)Decrease , decrease B e)Speed will only change if we change the frequency

If you were producing the sound with a speaker, as you changed the medium to increase the pressure amplitude, does driving the speaker become harder, easier or stay the same? a)Harder b)Easier c)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 2 b)Decreases by factor of 2 c)Stays the same d)Doubles e)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)1/9 b)1/3 c)1 d)3 e)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 = s m cos (kx-  t)  p =  p m sin (kx-  t)  p m = (v  ) s m  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 = P s /4  r 2 I =½  v  2 s m 2  The sound level is:  = (10 dB) log (I 0 /I)  Harmonic frequencies of a pipe f = nv/2L (open at 2 ends) f = nv/4L (open at 1 end)  Beat frequency = f beat = f 1 - f 2

Summary: Doppler Effect  Relative motion together produces an increase in frequency  Relative motion apart produces a decrease in frequency f’ = f ( v±v D / v±v S )