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Characteristics of Sound Waves


Characteristics of Sound Waves * * Transverse and Longitudinal Waves Classification of waves is according to the direction of propagation. In transverse waves the ... – PowerPoint PPT presentation

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Title: Characteristics of Sound Waves

Characteristics of Sound Waves
Transverse and Longitudinal Waves Classification
of waves is according to the direction of
propagation. In transverse waves the particles
vibrate perpendicular to the direction of
propagation (for example, a vibrating string or a
water wave) In longitudinal waves the particles
vibrate in the direction of propagation (for
example, an oscillating spring or sound waves)
The subject of sound is known in physics as
acoustics. One differentiates sound according to
the frequency as infrasonic, audible sound,
ultrasonic and hypersonic. Sonic infrasound is a
sound too low for humans to hear, below 20 Hertz.
Ultrasound is a sound too high for humans to
hear, above 20,000 Hertz.
We can obtain an equation of motion (a "wave
equation") for a particle on a stretched string
by applying Fma to a little piece of string.
When we do this, we find that a solution is any
function whose argument is x vt or x - vt. The
exact nature of the function f(x - vt) depends on
how the string is wiggled. When the end of a
string is wiggled like a harmonic oscillator, the
transverse displacement of the string is given by

air pressure
longitudinal wave
Speed of Sound A sound wave can be represented by
placing a long coiled spring on a horizontal
table. If one moves the end back and forth
harmonically, regions of compression and
rarefaction travel along the spring. The speed of
sound accounts for these changes in pressure and
can be written as an equation depending on its
elastic characteristics.
For which B is the bulk modulus and is the
mass density of the medium in which the sound is
Problems 1.) For steel the bulk modulus is
60?GPa and its density is 8 kgm-3. ?What is the
speed of sound in steel? Solution
2.) A wave is described as where
k 2.14 rad/m and ! 3.6 rad/s. Determine the
amplitude, wavelength, frequency, and speed of
the wave. Solution The amplitude is given. It is
2.10 cm. The wavelength is The frequency f is
The speed is
Superposition of Waves If wave displacements
are added together the resulting wave can show
either constructive or destructive interference.
If two waves of the same velocity and
wave- lengths are travelling in the same
direction, they will interfere. If they are in
phase they interfere constructively and result
in a stronger wave. If they are out of phase
and have the same amplitude, they cancel each
other out (destructive interference ).
Superposition of Waves
Two waves of the same phase
Two waves with equal but opposite phase
Constructive Interference
Destructive Interference
Standing Waves A standing wave is the result of
two waves of the same frequency and amplitude
moving in opposite directions to each other. A
mechanical example is a string that one wiggles
up and down and produces a propagating wave. If
one end is fixed, the wave will be reflected. As
a result, one cant observe a propagating wave
and instead the string experiences an oscillation
in one place. The antinodes will remain fixed and
the nodes will oscillate with a larger amplitude.
The distance between two nodes or antinodes is
the half wavelength of the original wave. Thus
for nodes we have the equation
Nodes The distance L of a crest from the center
is a half multiple of the wavelength.

with n 1, 2, 3 ...
Antinodes The distance L of a node from the
center is a multiple of the wave length plus a
with n 1, 2, 3 ...
Harmonics of Standing Waves
1st Harmonic
2nd Harmonic
3rd Harmonic
Beats If two travellng waves have slightly
different frequencies, they interfere and produce
a phenomen called beats.
The Doppler Effect The doppler effect
is the change in perceived or measured frequency
as the observer and the source travel relative to
one another of any kind of wave.
If the observer and the source move towards each
other, the frequency perceived by the observer
increases, if they move apart the frequency
decreases. For example, the sound of an ambulance
gets higher as it gets nearer and the tone gets
lower as it moves away. Observer at rest and
source of the signal moves Observer moves and
source of the signal at rest. The spacing of the
crests of the waves coming towards you is