# Music Physics 202 Professor Lee Carkner Lecture 10.

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Music Physics 202 Professor Lee Carkner Lecture 10

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  Want  L to be 0.15 m   Constructive interference occurs when  L = 0, 1, 2 …  L 2 = 4 m (or 4.3 m or 3.7 m etc.)

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

Intensity of Sound  I = P/A  The units of intensity are W/m 2  The intensity can be expressed as: I = ½  v  2 s m 2   Depends directly on  and v (medium properties)  Depends on the square of the amplitude and the frequency (wave properties)

Intensity and Distance   As you get further away from the source the intensity decreases because the area over which the power is distributed increases  The total area over which the power is distributed depends on the distance from the source, r I = P/A = P s /(4  r 2 )   I falls off as 1/r 2 (inverse square law)

Inverse Square Law Source r 2r A 1 =4  r 2 I 1 = P s /A 1 A 2 =4  (2r) 2 = 16  r 2 = 4A 1 I 2 = P s /A 2 = ¼ I 1

The Decibel Scale   To conveniently handle such a large range, a logarithmic scale is used known as the decibel scale  = (10 dB) log (I/I 0 )   I 0 = 10 -12 W/m 2 (at the threshold of human hearing)   There is an increase of 10 dB for every factor of 10 increase in intensity

Sound Levels  Hearing Threshold   Whisper   Talking   Rock Concert   Pain 

Human Sound Reception  Humans are sensitive to sound over a huge range   Your hearing response is logarithmic   Thus the decibel scale  Why logarithmic?   Similar to eyesight  Your ears are also sensitive to a wide range of frequencies   You lose sensitivity to high frequencies as you age

Music  A musical instrument is a device for setting up standing waves of known frequency   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   Closed end is like a tied end of string, open end is like a string end fixed to a freely moving ring

Sound Waves in a Tube

Harmonics  Pipe open at both ends   Antinode at both ends L = ½ n v = f f = nv/2L   Pipe open at one end   Node at one end, antinode at other L = ¼ n v = f f = nv/4L  n = 1,3,5,7 … (only have odd harmonics)

Harmonics in Closed and Open Tubes

Beat Frequency   If you listen to them simultaneously you hear variations in the sound at a frequency equal to the difference in frequency of the original two sounds called beats

Beats

Beats and Tuning   Compare the instrument to a standard frequency and adjust so that the frequency of the beats decrease and then disappear 

Next Time  Read: 17.9-17.10  Homework: Ch 17, P: 17, 30, 42, 50, 51