Question

A weight is attached to the free end of a sonometer wire. Resonance occurs at a length of 40 cm of the wire with a tuning fork of frequency 512 Hz. The weight is then immersed wholly in water, the resonant length is reduced to 30 cm. The relative density of the weight is

Solution

Correct option is

16/7

 

Let M be the mass attached to the end of the sonometer wire, then the tension in the wire is W = Mg. The frequency of the wire V is 512 Hz when its vibrating length is L = 40 cm. i.e. 

                           

When the mass is immersed in water, its weight reduces to W’due to upthrust; the vibrating length now becomes L’ = 30 cm.

 Now, the relative density of the solid is given by 

         

            

SIMILAR QUESTIONS

Q1

A tuning fork of frequency 480 Hz produces 10 beats per second when sounded with a vibrating sonometer string. What must have been the frequency of the string if a slight increase in the tension of the string produces fewer beats per second than before?

Q2

A train blowing its whistle moves with a constant velocity u away from the observer on the ground. The ratio of the actual frequency of the whistle to that measured by the observer is found to be 1.2. If the train is at rest and the observer moves away from it at the same velocity, the ratio would be given by

Q3

The intensity of sound gets reduced by 20% on passing through a slab. The reduction in intensity on passage through two consecutive slabs is

Q4

 

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are situated very near to the ears of a person who will hear

Q5

An organ pipe P1, closed at one end vibrating in its first harmonic and another pipe P2, open at both ends vibrating in its third harmonic, are in resonance with a given tuning fork. The ratio of the lengths of P1 and P2is

Q6

Two identical straight wires are stretched so to produce 6 beats per second when vibrating simultaneously. On changing the tension slightly in one of them, the beat frequency remains unchanged. Denoting by T1 andT2 the higher and the lower initial tensions in the strings, then it could be said that while making the above changes in tension.

Q7

The time taken by a particle executing simple harmonic motion of time period T to move from the mean position to half the maximum displacement is

Q8

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Q9

One end a long metallic wire of length L is tied to the ceiling. The other end is tied to a massless spring of spring constant K. A mass m hangs freely from the free end of the spring. The area of cross-section and Young’s modulus of the wire are A and Y respectively. If the mass is slightly pulled down and released, it will oscillate with a time period given by

Q10

A particle is executing simple harmonic motion along the x-axis with amplitude 4 cm and time period 1.2 s. The minimum time taken by the particle to move from x = +2 cm to x = +4 cm and back again is