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 strings were in unison?

Solution

Correct option is

800 Hz

 

Let T1 be the tension in each strings when they are in unison. Let T2 be the tension in each string when they are not in unison; then since  such that 

                           

                         

Expanding binomially, we have  Thus 

                         

Also,        

                 

Which gives V1 = 800 Hz.

SIMILAR QUESTIONS

Q1

An observer is at a distance of one metre from a point light source whose power output is 1 kW. Calculate the magnitude of electric and magnetic fields assuming that the source is monochromatic, it radiates uniformly in all directions and that at the point of observation it behaves like a travelling plane wave. Given that H/m and 

Q2

A wave pulse starts propagating in +x-direction along a non-uniform wire of length 10 m with mass per unit length given m = m0 + αx and under a tension of 100 N. Find the time taken by the pulse to travel from the lighter end (x = 0) to the heavier end. (m0 = 10–2 kg/m and α = 9 × 10–3 kg/m2)

Q3

Decibel is:

Q4

The variation of the speed of sound with temperature is greatest in:

Q5

The speed of sound in hydrogen at STP is v. The speed of sound in a mixture containing 3 parts of hydrogen and 2 parts of oxygen at STP will be 

Q6

The speed of sound in hydrogen at STP is v. What is the speed of sound in helium at STP?

Q7

Nine tuning forks are arranged in order of increasing frequency. Each tuning fork produces 4 beats per second when sounded with either of its neighbours. If the frequency of the 9th tuning fork is twice that of the first, what is the frequency of the first tuning fork?

Q8

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?

Q9

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

Q10

Two identical flutes produce fundamental notes of frequency 300 Hz at 27oC. If the temperature of the air in one flute is increased to 31oC, the number of beats heard per second will be