Question

Two identical strings of a stringed  musical instrument are in unison when stretched with the same tension. When the tension in one string is increased by 1%, the musician hears 4 beats per second. What was the frequency of the note when the string were in unison?

Solution

Correct option is

800 Hz

 

Let T1 be the tension in each strings which  such that

                               

                               

Expanding binomially, we have  Thus

                             

Also,             v2 – v1 = 4           or      v2 = v1 + 4. Therefore,

We have

                          

Which gives v1 = 800 Hz.

SIMILAR QUESTIONS

Q1

A sonometer wire of length 120 cm is divided into three segments of lengths in the ratio of 1 : 2 : 3. What is the ratio of their fundamental frequencies?

Q2

A particle is in linear simple harmonic motion between two extreme pointsA and B, 10 cm apart (see fig). If the direction from A to B is taken as positive direction, what are signs of displacement x, velocity V and acceleration a, when the particle is at A  

                                                

Q3

A simple harmonic motion of amplitude A has a time period T. The acceleration of the oscillator when its displacement is half the amplitude is

Q4

A body oscillates harmonically with amplitude 0.05 m. At a certain instant of time its displacement is 0.01 m and acceleration is 1.0 ms-2. What is the period of oscillation?

Q5

A tuning fork produces 4 beta per second when sounded with sonometer of vibrating length 48cm. It produces 4 beats per second also when the vibrating length is 50cm. What is the frequency of the tuning fork?

Q6

 

The displacement x (in centimetres) of an oscillating particle varies with time t (in seconds) as 

                         

The magnitude of the maximum acceleration of the particle is 

Q7

A particle executes SHM of amplitude 25 cm and time periods 3 s. what is the minimum time required for the particle to move between two points located at 12.5 cm on either side of the mean position?

Q8

A body executing linear simple harmonic motion has a velocity of 3 cms–1when its displacement is 4 cm and a velocity of 4 cms–1 when its displacement is 3 cm. what is the amplitude of oscillation?  

Q9

A particle is executing linear simple harmonic motion of amplitude A. what fraction of the total energy is kinetic when the displacement is half the amplitude?

Q10

A horizontal platform is executing simple harmonic motion in the vertical direction of frequency v. A block of mass m is placed on the platform. What is the maximum amplitude of the platform so that the block is not detached from it?