Embibe Experts Solutions for Chapter: Wave Motion on a String, Exercise 2: BEGINNER'S BOX - 2

A travelling wave in stretched string is given by the equation $y=40 \cos (3x–5t) \mathrm{cm}$ where $t$ is in $\sec$. Determine the maximum speed of particles of medium.

The displacement produced by a simple harmonic wave is $y=\frac{10}{\pi }\sin \left(200\pi t-\frac{\pi x}{17}\right)$. Then find the time period and maximum velocity of the particle. $(x\to \mathrm{m}, y\to \mathrm{cm}, t\to \sec )$

In the given figure, the string has mass $4.5 \mathrm{g}$. Find the time taken by a transverse pulse produced at the floor to reach the pulley $(g=10 {\mathrm{ms}}^{-2}).$

A wave moves with speed $300 {\mathrm{ms}}^{-1}$ on a wire which is under a tension of $500 \mathrm{N}$. Find how much the tension must be changed to increase the speed to $360 {\mathrm{ms}}^{-1}$.

A string of mass $2.50 \mathrm{Kg}$ is under a tension of $200 \mathrm{N}$. The length of the stretched string is $20.0 \mathrm{m}$. If the transverse jerk is struck at one end of the string, how long does the disturbance take to reach the other end?

A uniform rope of mass $0.1 \mathrm{kg}$ and length $2.45 \mathrm{m}$ hangs from a ceiling as shown in diagram.

(a) Find speed of transverse wave in the rope at a point $0.5 \mathrm{m}$ distance from the lower end.

(b) Calculate time taken by a transverse wave to travel the full length of rope.