Physics 123

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 0 0 C and 343 m/s at 20 0 C An echo is a reflected sound wave Loudness is related to intensity (W/m 2 ) 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 / I o = ( r o / r ) 2 Note: Humans can hear from 1 W/m 2 to W /m 2

Decibels dB = 10 log I / I o

Example Decibels The sound intensity of soft radio music is W /m 2 and I o = W /m 2. How loud is the radio in dB?

Solution Decibels dB = 10 log I / I o dB = 10 log (10 -8 / ) dB = 10 log 10 4 dB = 10 x 4 40 dB

Standing Waves on a String

Tube Closed at one end

Tube open at both ends

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 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

Solution Organ Pipe L = 3 / 2 and v = f So v = (2L/3)(f) 343 = (2L/3)(1000) L = 0.5 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 out of phase Same frequency

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

Temporal Interference - Beats In phase out of phase f1f1 f2f2

Problem 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 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 The change in the frequency of a moving source of sound

Doppler Effect This may sound like this! f1f1 f2f2

Doppler Effect Observer approaching f ' = f ( 1 + V O / V) Observer receding f ' = f ( 1 - V O / V) Source approaching f ' = f / ( 1 - V S / V) Source receding f ' = f / ( 1 + V S / V)

That’s all folks!