Question

The rope of the length 6 m is fixed to a vertical wall in the horizontal x-direction. We send one transverse pulse on a rope in a vertical +y direction towards and it returns back in 3 s (total time, ie. return trip). Which statement is correct?

Answer 1

Answer:

The pulse return in -y direction, the speed of the pulse is 4 m/s.

(Iv) is correct option.

Explanation:

Given that,

Length of rope = 6 m

Total time = 3 sec

Suppose, statements are

(I). The pulse return in+ y direction, the speed of the pulse is 2 m/s.

(II). The pulse return in+ y direction, the speed of the pulse is 4 m/s.

(III). The pulse return in- y direction, the speed of the pulse is 2 m/s.

(Iv). The pulse return in- y direction, the speed of the pulse is 4 m/s.

We send one transverse pulse on a rope in a vertical +y direction towards and it returns back -y direction

We need to calculate the speed of wave

Using formula of speed

$v =\dfrac{D}{t}$

$v=\dfrac{d_{1}+d_{2}}{t}$

Where, $d_{1}$ = length of rope in +y direction

$d_{2}$ = length of rope in -y direction

$v=\dfrac{6+6}{3}$

$v=4\ m/s$

The speed of the pulse is 4 m/s.

Hence, The pulse return in -y direction, the speed of the pulse is 4 m/s.