Waves

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Waves
A pulse on a string (demos) speed of pulse wave
speed v depends upon tension T and inertia
(mass per length m) y f(x-vt) (animation)
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Periodic Waves coupled harmonic motion
(animations) aka sinusoidal (sine)
waves wave speed v the speed of the wave, which
depends upon the medium only. wavelength l the
distance over which the wave repeats, frequency
f the number of oscillations at a given point
per unit time. T 1/f. distance between crests
wave speed ? time for one cycle l vT -gt
Wavelength, speed and frequency are related
by v l f
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Mathematical Description of Periodic Waves
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The Wave Equation
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Transverse Wave Velocity lifting the end of a
string Tension F Linear Mass Density (m/L)
m Transverse Force Fy
Fnet
vt
vyt
Fy
F
F
l vt
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Reflections at a boundary fixed end hard
boundary
Pulse is inverted
Reflections at a boundary free end soft
boundary
Pulse is not inverted
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Reflections at an interface light string to heavy
string hard boundary faster medium to slower
medium
heavy string to light string soft
boundary slower medium to faster medium
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Principle of Superposition When Waves
Collide! When pulses pass the same point, add
the two displacements (animation)
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Standing Waves vibrations in fixed
patterns effectively produced by the
superposition of two traveling waves y(x,t)
(ASW sin kx) coswt constructive interference
waves add destructive interference waves cancel
3l 2L
l 2L
2l 2L
4l 2L
node
antinode
antinode
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Example The A string on a violin has a linear
density of 0.60 g/m and an effective length of
330 mm. (a) Find the Tension in the string if
its fundamental frequency is to be 440 Hz. (b)
where would the string be pressed for a
fundamental frequency of 495 Hz?
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Standing Waves II pipe open at one end