Question

Two strings are adjusted to vibrate at exactly 200 Hz. Then the tension in one string is increased slightly. Afterward, three beats per second are heard when the strings vibrate at the same time. What is the new frequency of the string that was tightened?

Short answer

The new frequency of the string is 203Hz

Step-by-step solution

Step1. Write the given information

Frequency of the strings f= 200Hz

The tension of one string is increased

The beats heard when strings vibrate at the same time n=3

To determine the new frequency 

Beats are produced when two waves of the same or slightly different frequencies travel in the same medium simultaneously. The super-positioned waves form beats and the number of beats produced per second is called beat frequency and they are equal to the difference in the frequency of the two waves.

The frequency of the string is given by

$f=\frac{1}{2L}\sqrt{\frac{T}{\mu }}$

Here,

L = length of the string

T= tension in the string

µ = mass per unit length

Let the new frequency of the string after the tension is increased is given by f’

According to the question

$$\begin{gathered} f’-f=3 \\ f’=3+f \\ f’=3+200Hz \\ =203Hz \end{gathered}$$

Thus, the new frequency of the string is 203Hz