Question

A uniform rope of mass 6 kg hangs vertically from a rigid support. A block of mass 2 kg is attached to the free end of the rope. A transverse pulse of wavelength 0.06 m is produced at the lower end of the rope. The wavelength of the pulse when it reaches the top is (in m):

Solution

Correct option is

0.12

 

The speed of transverse waves through a string of linear density m and tension T is given by:

                         

Since f and m are constants, v and hence λ is proportional to  The tension at the bottom is 2 kg wt, while at the top is 2 + 6 = 8 kg wt. If λ1and λ2 are the wavelengths at the bottom and the top respectively, we have:

                       

The wavelength at the top will be = 0.12 m.

SIMILAR QUESTIONS

Q1

The fundamental frequency of a longitudinal vibrating of a rod clamped at its centre is 1500 Hz. If the mass of the rod is 96 g the increase in its total length produced by a stretching force of 10 kg weight will be:

Q2

If there are three sources of sound of equal intensity with frequencies 300, 301 and 302, the number of beats heard per second will be:

Q3

The speed of sound waves in dry air at NTP is 332 m/sec. Assuming air to be composed of oxygen and nitrogen in the ratio 1:4 and the densities of oxygen and nitrogen at NTP to be in the ratio 8:7, the velocity of sound in oxygen will be equal to:

Q4

The speed of sound waves in a mixture of helium and neon at 300 K and at a pressure of 76 cm of Hg was found to be 758 m/sec. The densities of helium and neon are respectively 0.1785 and 0.8999 g/litre and γ of mixture is 1.667. What is the ratio of He and Ne in the mixture?

Q5

The number of possible overtones of air column in a closed pipe of length 83.2 cm and of diameter 6 cm whose frequencies lie below 1000 Hz will be [velocity of sound = 340 m/s]:

Q6

Two stars P and Q have slightly different surface temperatures TP and TQrespectively, with TP > TQ. Both stars are receding from the earth with speeds vP and vQ relative to the earth. The wavelength of light at which they radiate the maximum energy is found to be same for both:

Q7

In a resonance column experiment, a long tube, open at the top, is calmed vertically. By a separate device, water level inside the tube can be moved up or down. The section of the tube from the open end to the water level acts as a closed organ pipe. A vibrating tuning fork is held above the open end, and the water level is gradually pushed down. The first and the second resonances occur when the water level is 24.1 cm and 74.1 cm respectively below the open end. The diameter of the tube is:

Q8

A wave represented by the equation  is superimposed on another wave to form a stationary wave such that the point x = 0 is a node. The equation for the other wave is:   

Q9

The amplitude of a wave disturbance propagating in the positive x-direction is given by  at time t = 0 and by  at t = 2 seconds, where x and y are in metres. The shape of the wave disturbance does not change during the propagation. The velocity of the wave is:       

Q10

A tuning fork of frequency 256 Hz is excited and held at the mouth of a resonance column of frequency 254 Hz. Choose the correct statement: