Question

Solution

Correct option is

95 Hz

Let N be the frequency of the tuning fork. Then, the frequency of the wire, when the tension is 100 N will be (N + 5) and when the tension is 81 N, it is (N – 5); since in each case 5 beats are heard per second. Hence  subtracting (ii) from (i) we have Using this value of m in (i) or (ii) gives N = 95 Hz.

SIMILAR QUESTIONS

Q1

Standing waves are produced by the superposition of two waves and Where x and y are expressed in metres and t is in seconds. What is the amplitude of a particle at x = 0.5 m. Given Q2

The transverse displacement of a string fixed at both ends is given by Where x and y are in metres and t is in seconds. The length of the string is 1.5 m and its mass is 3.0 × 10–2 kg. What is the tension in the string?

Q3

A wire of density ρ is stretched between two clamps a distance L apart, while being subjected to an extension lY is the Young’s modulus of the material of the wire. The lowest frequency of transverse vibrations of the wire is given by

Q4

A pipe of length 20 cm is closed at one end. Which harmonic mode of the pipe is resonantly excited by a 425 Hz source? The speed of sound = 340 ms –1.

Q5

A pipe of length 20 cm is open at both ends. Which harmonic mode of the pipe is resonantly excited by a 1700 Hz source? The speed of sound = 340 ms–1

Q6

A wire has a mass 30 g and linear density 4 × 10 –2 kg m–1. It is stretched between two rigid supports and vibrates in its fundamental mode with a frequency of 50 Hz. What is the speed of transverse waves on the wire?

Q7

A steel rod of length 1.0 m is clamped rigidly at its middle. What is the frequency of the fundamental mode for the longitudinal vibrations of the rod? The speed of sound in steel = 5 × 103 ms –1

Q8

Two tuning forks A and B produce 10 beats per second when sounded together. On slightly loading fork A with a little wax, it was observed that 15 beats are heard per second. If the frequency of fork B is 480 Hz, what is the frequency of fork A before it was loaded?

Q9

Two sitar strings A and B are slightly out of tune and produce beats of frequency 6 Hz. When the tension in string A is slightly decreased, the beat frequency is found to be reduced to 3 Hz. If the original frequency of A is 324 Hz, what is the frequency of B?

Q10

An ambulance blowing a siren of frequency 700 Hz is travelling slowly towards a vertical reflecting wall with a speed of 2 ms–1. The speed of sound is 350 ms–1. How many beats are heard per second?