Question

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?

Solution

Correct option is

318 Hz

 

  

The frequency of string B is   

              

Now, the frequency of a string is proportional to the square root of tension. Hence, if the tension in A is slightly decreased, its frequency will be slightly reduced, i.e. it will become less that 324 Hz. If the frequency of string B is 330 Hz, the beat frequency would increase to a value greater than 6 Hz if the tension in A is reduced. But the beat frequency is found to decrease to 3 Hz. Hence, frequency of B cannot be 330 Hz; it is, therefore 318 Hz. When the tension in A is reduced, its frequency becomes 324 – 3 = 321 Hz which will produce beats of frequency 3 Hz with string B of frequency 318 Hz.

SIMILAR QUESTIONS

Q1

A uniform metal wire of density ρ, cross-sectional area A and length L is stretched with a tension T. The speed of transverse wave in the wire is given by

Q2

 

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 

Q3

 

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?

Q4

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

Q5

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.

Q6

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 

Q7

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?

Q8

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 

Q9

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?

Q10

A metal wire of diameter 1 mm is held on two knife edges separated by a distance of 50 cm. The tension in the wire is 100 N. The wire vibrating with its fundamental frequency and a vibrating tuning fork together produce 5 beats per second. The tension in the wire is then reduced to 81 N. When the two are excited, beats are heard at the same rate. What is the frequency of the fork?