A hand holding a rope moves up and down to create a transverse
wave on the rope. The hand completes an oscillation in 3 s, and the
wave travels along the string at 0.6 m/s. The amplitude of the wave
is 0.09m.
a.) Find the frequency at which the crests pass a
given point in space.
Hz
b.) Find the distance between two adjacent crests
on the wave.
m
c.) There is a blue spot drawn onto the rope with
a pen. Find the distance this spot travels in one period.
m
d.) If the mass per unit length of the string is
7·10-4 kg/m, what is the tension in the string?
N
a) The same as the hand frequency
f = 1/3 = .0.33 /s
f = 0.33 Hz
b)
We know,
Frequency * wavelength = speed
wavelength = Speed/frequency
wavelength = 0.6/0.33
wavelength = 1.82 m
Distance between two adjacent crests on the wave, =
Wavelngth = 1.82 m
c)
The dot travels upwards then comes back to the middle, then
downards, and again back to the middle in one period.
Therefore total Distance travelled = 4 * 0.09m = 0.36
m
Total Distance travelled = 0.36 m
d) velocity = sqrt(Tension / linear mass)
0.6 m/s = sqrt(T / (7*10^-4 kg/m)),
Solving for T
T = 2.52 * 10^-4 N
Tension in the String, T = 2.52 * 10^-4 N
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