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

Question

1.A hand holding a rope moves up and down to create a transverse wave on the rope. The hand completes an oscillation in 1.5 s, and the wave travels along the string at 0.8 m/s. The amplitude of the wave is 0.1 m.

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 8·10-4 kg/m, what is the tension in the string?
N

Explanation / Answer

a) T = 1.5s, so f = 1/T = (1/1.5s) = 0.67Hz

b) If the wave speed is v, then f = v, and = v/f = 0.8m/s / 0.67Hz = 1.19m

c) It would travel one wavelength forwards and four amplitudes up and down (1 up, 2 down, 1 up), which gives us a total distance of

d = ((1.19m)^2 + (0.4m)^2 ) = 1.26m

d) v = (F/), so

F = v^2 * = (0.8 m/s)^2 * (8*10^-4 kg/m) = 0.000512N = 5.12*10^-4 N

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