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
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)
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