## Question

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 *T*_{1} and*T*_{2} the higher and the lower initial tensions in the strings, then it could be said that while making the above changes in tension.

### Solution

*T*_{2} was increased & *T*_{1} was decreased

Let *V*_{1} be the frequency of the wire having tension *T*_{1} and *V*_{2} that of wire having tension *T*_{2}. Since and it follows that . Given *V*_{1} – *V*_{2} = 6. Now, if *V*_{1} is decreased by 12 Hz to a value remains unchanged, the number of beats per second would be Also if *V*_{2} is increased by 12 Hz to a value remains unchanged, then the number of beats per second would be Hence, the beat frequency will remain unchanged if either *T*_{1} is decreased or *T*_{2} is increased.

#### SIMILAR QUESTIONS

Two bodies *M* and *N* of equal masses are suspended from two separate springs of force constants *k*_{1} and *k*_{2} respectively. If they oscillate with equal maximum velocities, the amplitudes of *M* and *N* will be the ratio of

A sonometer wire is in unison with a tuning fork. Keeping the tension unchanged, the length of the wire between the bridge is doubled. The tuning fork can still be in resonance with the wire, provided the wire now vibrates in

A source of sound emitting a note of frequency 200 Hz moves towards an observer with a speed *v* equal to the speed of sound. If the observer also moves away from the source with the same speed *v*, the apparent frequency heard by the observer is

The difference between the apparent frequencies of a source of sound as perceived by an observer during its approach and recession is 2% of the actual frequency of the source. If the speed of sound in air is 300 ms^{–1}, the speed of the source is

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?

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

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

Two sounding bodies producing progressive waves given by

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

An organ pipe *P*_{1}, closed at one end vibrating in its first harmonic and another pipe *P*_{2}, open at both ends vibrating in its third harmonic, are in resonance with a given tuning fork. The ratio of the lengths of *P*_{1} and *P*_{2}is

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