Home
Class 11
PHYSICS
Three pieces of string, each of length L...

Three pieces of string, each of length L, are joined together end-to-end, to make a combined string of length 3L. The first piece of string has mass per unit length `mu_1`, the second piece has mass per unit length `mu_2 = 4mu_1` and the third piece has mass per unit length `mu_3 = mu_1//4` .
(a) If the combined string is under tension F, how much time does it take a transverse wave to travel the entire length 3L? Give your answer in terms of L,F and `mu_1` .
(b) Does your answer to part (a) depend on the order in which the three piece are joined together? Explain.

Text Solution

Verified by Experts

The correct Answer is:
A, B
(a) `v_1 = sqrt (T//mu_1)`
` v_2 = sqrt (F//4mu_1) = 1/2 sqrt(F//mu_(1))`
`v_3 = sqrt (F//(mu_1//4)) = 2 sqrt(F//mu_1)`
` :. T = t_1 + t_2 + t_3 = L/ v_1 + L/v_2 + L/v_3`
= (7L)/2 sqrt (mu_1/F)` .
Promotional Banner

Topper's Solved these Questions

  • SUPERPOSITION OF WAVES

    DC PANDEY|Exercise Level 2 Comprehension Based|3 Videos

  • SOUND WAVES

    DC PANDEY|Exercise Exercise 19.7|4 Videos

  • THERMOMETRY THERMAL EXPANSION AND KINETIC THEORY OF GASES

    DC PANDEY|Exercise Medical entrance gallary|30 Videos

Similar Questions

Explore conceptually related problems

Four pieces of string of length L are joined end to end to make a long string of length 4L. The linear mass density of the strings are mu,4mu,9mu and 16mu , respectively. One end of the combined string is tied to a fixed support and a transverse wave has been generated at the other end having frequency f (ignore any reflection and absorption). string has been stretched under a tension F . Find the time taken by wave to reach from source end to fixed end.

The frequency of vibration of string depends on the length L between the nodes, the tension F in the string and its mass per unit length m. Guess the expression for its frequency from dimensional analysis.

A stretched string of length L fixed at both the ends has nodes, where n gt 2 . What is the length of the string in terms of n and lambda ?

A straight rod of length L has one of its end at the origin and the other at X=L . If the mass per unit length of the rod is given by Ax where A is constant, where is its centre of mass?

String-1 is connected with string-2 The mass per unit length in string-1 is mu _1 and mass per unit length in string-2 is 4mu _1. The tension in the strings is T .A travelling wave is coming from the left .What fraction of the energy in the incident wave goes into string-2?

Derive an expression for the velocity of pulse in a in stretched in string under a tension T and mu is the mass per unit length of the sting.

A string consists of two parts attached at x=0 , The right part of the string (xlt 0) has mass per unit length mu_r and the left part of the string (xlt 0) has mass per unit length mu _l The tension in the string is T. If a wave of units amplitude travels along the left part of the string,what is the amplitude of the wave that is transmitted to the right part of the string?

The speed of transverse wave v in a stretched string depend on length tension T in the string and liner mass density (mass per unit length). mu . Find the relation using method of dimensions.

A piano string having a mass per unit length equal to 5.00 xx 10^(3)kg//m is under a tension of 1350 N , Find the speed with which a wave travels on this string.

A ribbon of length 5(1/4) m is cut into small pieces each of length 3/4 Number of pieces will be: