First slide

Stationary waves

Question

If the length of a stretched string is shortened by 40% and the tension is increased by 44%, then the ratio of the final and initial fundamental frequencies is

Moderate

A

2 : 1
B

3 : 2
C

3 : 4
D

1 : 3

Solution

Fundamental frequency in case of string is
$n = \frac{1}{2 l} \sqrt{\frac{T}{m}} \Rightarrow n \propto \frac{\sqrt{T}}{l} \Rightarrow \frac{n'}{n} = \sqrt{\frac{T'}{T}} \times \frac{l}{l'}$
putting $T' = T + 0 .44 T = \frac{144}{100} T and l' = l - 0 .4 l = \frac{3}{5} l$
We get $\frac{n'}{n} = \frac{2}{1}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App