Calculate the speed
of 25 cm ripples
passing through
water at 120
waves/s
Determine the l, f, &
th
T of the 49 overtone
of a 4.0 m organ pipe
when vsound = 350.0
m/s
Chapter 15
Sound
Sound Waves
Longitudinal waves caused
by pressure change
producing compressions
& rarefactions of particles
in the medium
Sound Waves
Any vibrations produce
regular oscillations
pressure as the vibrating
substance pushes air
molecules back & forth
Sound Waves
The oscillating air
molecule collide with
others transmitting the
pressure variations away
from the source
Sound Waves
Air 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
o
m/s C)(T)
Speed of Sound
vsound ~ 343 m/s
At room temp.
o
25 C
Speed of Sound at
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 l 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
o
frequencies at 30.83 C:
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 Displacementnode
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
l = 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
l0 = 4L
l1 = 4L/3
l2 = 4L/5
Wavelengths Generated
by an Open Pipe
Resonator
l= 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
l0 = 2L
l1 = 2L/2
l2 = 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 l, f, &
th
T of the 19 overtone
of a 50.0 cm open
tube when vsound =
350.0 m/s
Determine the l, f, &
th
th
T of the 9 & 14
overtone of a 80.0 cm
open tube when vsound
= 350.0 m/s
Determine the l, f, & T
st
of the fundamental & 1
three overtones of a
700.0 mm open tube
when vsound = 350.0 m/s