EXPERIMENT 6
WAVE PROPAGATION AND STANDING WAVES
Measure the velocity of sound in air by measuring the resonances of a tube closed at both
ends.
Traveling Waves
Homework:
1) Read the “notes for experiment 6” on the webct site.
2) The relation between frequency wavelength and velocity of propagating waves:
A traveling wave is described by the function
)
sin(
0
t
kx
y
y
ϖ

=
The quantity which oscillates in the wave (pressure in an acoustic wave, water height in a
water wave, electric field in a radio wave, etc.) is represented as
y
. The “amplitude” of
the wave (half of the peak to peak variation) is
y
0
.
The frequency in radians/sec is
ϖ
and
is
f
=
ϖ
/2
π
in Hz.
The wave number,
k
, is equal to 2
π
/
λ,
where
λ
is the wavelength.
a) Using the above expression for a traveling wave, show that at any given time, the
shortest distance between two places where
y
= 0,
is
∆
x =
π
/
k
=
λ
/2.
b) Show that at a fixed position,
x
=
λ
/4, the shortest time between equal values of
y,
with
y
increasing, is 1/(
f
)
c) Show that the location along the x axis for which
2
0
y
y
=
moves at velocity,
v
=
ϖ/
k
.
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 Spring '08
 Bodde
 Work, Wavelength, tc, Standing wave, frequency sound wave

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