A hand holding a rope moves up and down to create a transverse wave on the rope.

Question

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

Explanation / Answer

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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