Question

A taut string having tension $100 N$ and linear mass density $0.25 kg / m$ is used inside a cart to generate a wave pulse starting at the left end, as shown. What should be the velocity of the cart so that pulse remains stationary w.r.t. ground.

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Accepted Answer

The expression $v = \sqrt{\frac{T}{μ}}$ gives the velocity of the wave in

the string. Here the string is moving with cart.

Velocity of pulse $v = \sqrt{\frac{T}{μ}} \Rightarrow \frac{100}{0.25} = 20 m s^{- 1}$

This velocity is w.r.t. car.

Velocity of the pulse can be given as

${\vec{v}}_{P} = {\vec{v}}_{PC} + {\vec{v}}_{CG}$

Where, ${\vec{v}}_{PC}$ is velocity of pulse with respect to cart and ${\vec{v}}_{CG}$ is velocity of cart with respect to ground.

$0 = 20 i + {\vec{v}}_{CG}$

${\vec{v}}_{CG} = - 20 i m s^{- 1}$

Hence, the cart should move with velocity $20 m s^{- 1}$ in the direction opposite to the pulse.

B M Sharma Solutions for Chapter: Travelling Waves, Exercise 1: ILLUSTRATIONS

B M Sharma Physics Solutions for Exercise - B M Sharma Solutions for Chapter: Travelling Waves, Exercise 1: ILLUSTRATIONS

Questions from B M Sharma Solutions for Chapter: Travelling Waves, Exercise 1: ILLUSTRATIONS with Hints & Solutions

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