Calculate the speed of 25 cm ripples passing through

water at 120 waves/s

Determine the , f, & T of the 49th overtone of a 4.0 m organ pipe when vsound = 350.0

m/s

Chapter 15Sound

Sound WavesLongitudinal waves caused

by pressure change producing compressions

& rarefactions of particles in the medium

Sound WavesAny vibrations produce

regular oscillations pressure as the vibrating

substance pushes air molecules back & forth

Sound WavesThe oscillating air

molecule collide with others transmitting the

pressure variations away from the source

Sound WavesAir resistance will cause the amplitude of the wave

to diminish as it moves away from the source

Speed of Sound

vsound in air = 331.5 m/s

+ (0.60 m/soC)(T)

Speed of Sound

vsound ~ 343 m/sAt room temp.

Speed of Sound at 25oC

vin air = 343 m/s

vfresh water = 1493 m/s

vsea water = 1533 m/s

vin steel = 5130 m/s

The human ear can detect sound between

20 Hz & 16 kHz. Calculate the

wavelength of each:

Calculate the in mm of notes with

frequencies of:2.0 kHz & 10.0 kHz

vsound = 342 m/s

Loudness•How loud sound is, is proportional to the

amplitude of its waves

Decibels (dB)•Unit for measuring

the loudness of a sound wave

Decibels•Measured in log

units•50 dB is 10 x greater

than 40 dB

Pitch•Pitch is proportional

to the frequency or inversely

proportioned to the wavelength

Doppler Effect•Changes in observed

pitch due to relative motion between the

source & the observer of the sound wave

Doppler Effect•The pitch of

approaching objects has higher frequencies or shorter wavelengths

Doppler Effect•The pitch of objects

moving apart has lower frequencies or longer

wavelengths

The Physics of Music

Almost all musical instruments are some form of an

open tube or strings attached at two ends

In brass instruments, the lip vibrates against

the mouthpiece causing the instrument

to vibrate

In reed instruments, air moving over the

reed causes it to vibrate causing the

instrument to vibrate

In pipe instruments, air moving over the

opening causes air to vibrate causing the

instrument to vibrate

In stringed instruments, plucking the string causes it to vibrate

causing the instrument to vibrate

In musical instruments, the sound is dependent upon resonance in air

columns

In each instrument, the longest wavelength

produced is twice the length of string or air

column

Resonance•When multiple objects

vibrate at the same frequency or wavelength

Resonance•Resonance increases amplitude or loudness

as multiple sources reinforce the waves

Resonance•The length & width of the

air column determine the pitch (frequency or

wavelength)

Resonance•In instruments sound

resonates at a fundamental pitch and

many overtones

Calculate the wavelengths for each of

the following sound frequencies at 30.83oC:

4.0 MHz & 10.0 MHz

Fundamental•The lowest tone or frequency that can be

generated by an instrument

Overtones•Sound waves of higher frequency or pitch than

the fundamental

Pipe Resonance•Open Pipe: open at

both ends

•Closed Pipe: Closed at one end

Pipe: Open End•High Pressure-antinode

•Zero Displacement-node

Pipe: Closed End•Pressure node

•Displacement antinode

Closed Pipe Resonator

•A pipe that is closed at one end

Open Pipe Resonator

•A pipe that is open at both ends

Wavelengths Generated by a Closed Pipe

Resonator

= 4L/(2n +1)f = v(2n+1)/4L

Wavelengths Generated by a Closed Pipe

Resonator

n = 0 for the fundamental

Wavelengths Generated by a Closed Pipe

Resonator

n = positive integers for overtones

Typical Wavelengths Generated by CP

0 = 4L

1 = 4L/3

2 = 4L/5

Wavelengths Generated by an Open Pipe

Resonator

= 2L/(n+1)f = (n+1)v/2L

Wavelengths Generated by an Open Pipe

Resonator

n = 0 for the fundamental

Wavelengths Generated by an Open Pipe

Resonator

n = positive integers for overtones

Typical Wavelengths Generated by OP

0 = 2L

1 = 2L/2

2 = 2L/3

Calculate the longest wavelength & the first

two overtones produced using a 68.6 cm saxophone. (open)

Calculate the wavelengths &

frequencies of the longest & the first 4 overtones produced using a 2.0 m tuba.

Calculate the wavelengths & frequencies of the lowest & the first 4

overtones produced using a 5.0 cm whistle. (closed)

Sound Quality

Fundamental•The lowest tone or frequency that can be

generated by an instrument

Overtones•Sound waves of a higher frequency or

pitch than the fundamental

Harmonics•Sound waves of higher frequency or pitch than

the fundamental or overtones

Timbre•Quality of sound

•Addition of all harmonics generated

determines timbre

Beat•Oscillations in sound

wave amplitude

•Can be produced by wave reinforcement

Consonance•Several pitches produced simultaneously producing a pleasant sound called a:

Chord

Dissonance•Several pitches produced simultaneously producing an unpleasant sound or:

Dischord

Consonance•Consonance occurs when the frequencies having small whole

number ratios

Consonance Frequency Ratios

•2:3

•3:4

•4:5

Consonance Frequency Ratios

•The notes in the chord C major have frequency

ratios of 4:5:6

Octave•When two notes with a frequency ratio of 2:1, the higher note is one octave

above the lower note

Frequency Ratios•1:2 - octave

•2:3 - Perfect Fifth

•3:4 - Perfect Fourth

•4:5 - Major Third

Noise•A mixture of a large number of unrelated

frequencies

Determine the , f, & T of the 19th overtone

of a 50.0 cm open tube when vsound =

350.0 m/s

Determine the , f, & T of the 9th & 14th

overtone of a 80.0 cm open tube when vsound

= 350.0 m/s

Determine the , f, & T of the fundamental & 1st

three overtones of a 700.0 mm open tube

when vsound = 350.0 m/s