Question

A stone hangs from the free end of a sonometer wire whose vibrating length, when tuned to a tuning fork, is 40 cm. When the stone hangs wholly immersed in water, the resonant length is reduced to 30 cm. The relative density of the stone is

Solution

Correct option is

16/7

 

 where M = mass of stone. If ρ is the density of the stone andV its volume, then m = ρ V. When the stone is wholly immersed in water of density ρ, the effective weight of the stone

      

Given      l = 40 cm and l’ = 30 cm. Also V = V’, which gives  

                    

SIMILAR QUESTIONS

Q1

Transverse wave of amplitude 10 cm is generated at one end (x = 0) of a long string by a tuning fork of frequency 500 Hz. At a certain instant of time, the displacement of a particle A at x = 100 cm is – 5 cm and of particle B at x = 200 cm is +5 cm. What is the wavelength of the wave?

Q2

Transverse waves of the same frequency are generated in two steel wires A and B. The diameter of A is twice that of B and the tension in A is half that in B. The ratio of the velocities of waves in A and B is

Q3

A sonometer wire, with a suspended mass of M = 1 kg, is in resonance with a given tuning fork. The apparatus is taken to the moon where the acceleration due to gravity is 1/6 that on earth. To obtain resonance on the moon, the value of M should be

Q4

A source of sound vibrates according to the equation y = 0.05 cos π t. It sends waves of velocity 1.5 ms –1. The wavelength of the waves is    

Q5

Two identical waves, each of frequency 10 Hz, are travelling in opposite directions in a medium with a speed of 20 cm s–1. The distance between adjacent nodes is

Q6

Figure shows the shape of part of a long string in which transverse waves are produced by attaching one end of the string to tuning fork of frequency 250 Hz. What is the velocity of the waves?

                                                  

Q7

 

Particle displacements (in cm) in a standing wave are given by 

                     

The distance between a node and the next anti-node is

Q8

If Young’s modulus of the material of a rod is  and its density is 8000 kg m–3, the time taken by a sound wave to traverse 1 m of the rod will be 

Q9

An observer moves towards a stationary source of sound with a velocity one-tenth the velocity of sound. The apparent increase in frequency is

Q10

A cylindrical tube, open at both ends, has fundamental frequency n. If one of the ends is closed, the fundamental frequency will become