12. Sound
12.1 Characteristics of Sound
12.2 Intensity of Sound - Decibels
12.5 Vibrating Strings and Air Columns
12.7 Interference of Sound Waves - Beats
12.8 Doppler Effect
Characteristics of Sound
• Sound waves are longitudinal
• Speed of sound is different in different media
• Speed of sound in air is 331 m/s at 00C and 343 m/s at 200C
• An echo is a reflected sound wave
• Loudness is related to intensity (W/m2)
• Pitch is frequency of sound
• Humans can hear 20 Hz to 20,000 Hz
• Dogs and bats can hear the ultrasonic range
Intensity of Sound - Decibels
The intensity of sound decreases with distance from the source as the inverse square of the distance.
Double the distance and the intensity becomes a quarter.
I / Io = ( ro / r )2
Note: Humans can hear from 1 W/m2 to 10 -12 W /m2
Example 12.1 - Decibels
The sound intensity of soft radio music is 10 -8 W /m2 and Io = 10 -12 W /m2. How loud is the radio in dB?
Solution 12.1 - Decibels
dB = 10 log I / Io
dB = 10 log (10 -8 / 10 -12 )
dB = 10 log 104
dB = 10 x 4
40 dB
Standing Waves - Chart
String open tube closed tube
L = / 2 L = / 2 L = / 4
L = L = L = 3 / 4
L = 3 / 2 L = 3 / 2 L = 5 / 4
L = 2 L = 2 L = 7 / 4
L = 5 / 2 L = 5 / 2 L = 9 / 4
Odd and Even Harmonics Odd Harmonics
Example 12.2 - Organ Pipe
An organ pipe open at both ends vibrates in its third harmonic at a frequency of 1000 Hz. If the speed of sound is 343 m/s, the length of the pipe is most nearly
A. 0.3 m
B. 0.5 m
C. 0.7 m
D. 0.9 m
Interference
Constructive Interference: When two waves run into each other in step (in phase). The outcome is increased amplitude
Destructive Interference: When two waves run into each other out of step (out of phase). The outcome is decreased amplitude
Spatial Interference
In phase if path difference is an even multiple of
Out of phase if path difference is an odd multiple of
Path difference
Problem 12.3 . . . Blinking Lights
One car’s turn signal blinks 10 times in 10 seconds and another car’s blinks 15 times in 10 seconds. How often are they going to be in phase (sync)?
Solution 12.3 . . . Blinking Lights
Beat frequency = f 1 - f 2
The blinking lights will be in sync 5 times in 10 seconds or once every 2 seconds!
Doppler Effect
Observer approaching f ' = f ( 1 + VO / V)
Observer receding f ' = f ( 1 - VO / V)
Source approaching f ' = f / ( 1 - VS / V)
Source receding f ' = f / ( 1 + VS / V)