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 0.5 m/s. The amplitude of the wave is 0.05 m.

a.) Find the frequency at which the crests pass a given point in space.
0.33  Hz (this answer was correct)

b.) Find the distance between two adjacent crests on the wave.
1.51  m (this answer was correct)

c.) There is a blue spot drawn onto the rope with a pen. Find the distance this spot travels in one period.
(I have tried the following, all incorrect: 1.51 ; 1.5 ; 3.14; Please help me find the correct answer since all three listed are incorrect)

d.) If the mass per unit length of the string is 8·10-4 kg/m, what is the tension in the string?
2E-4 N (this was correct answer)

Explanation / Answer

here,

c)

time period , T = 3 s

v = 0.5 m/s

the distance travelled by the blue spot , d = 4 * amplitude

d = 4 * 0.05

d = 0.2 m

the distance travelled by spot in one period is 0.2 m

d)

mass per unit length , u = 8 * 10^-4 kg/m

velocity , v = sqrt( T /u)

0.5^2 = sqrt( T/( 8*10^-4))

T = 2 * 10^-4 N

the tension in the string is 2 * 10^-4 N

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