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.

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 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

Decibels

dB = 10 log I / Io

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 on a String

Node

AntinodeNode

Node

Antinode

= 2L/3

= L

= 2LL

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 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

Solution 12.2 - 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

f1

f2

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

The change in the frequency of a moving source of sound

Doppler Effect

This

may sound

like this!

f1

f2

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)

That’s all folks!