A string vibrates with a frequency of 200 Hz. When its length is doubled and tension is altered, it begins to vibrate with a frequency of 300 Hz. The ratio of the new tension to the original tension is

Question

Dr. Abubacker · Accepted Answer

(a) Frequency
$v = \frac{1}{2\iota}\sqrt{\frac{T}{m}}$
$\Longrightarrow \ \ \ \ \ \ v \propto \frac{\sqrt{T}}{\iota}$
$\frac{T_{2}}{T_{1}} = \left\lbrack \frac{v_{2}}{v_{1}} \right\rbrack^{2}\left\lbrack \frac{\iota_{2}}{\iota_{1}} \right\rbrack^{2}$
$= \left\lbrack \frac{300}{200} \right\rbrack^{2}\left\lbrack \frac{2\iota}{\iota} \right\rbrack^{2} = \frac{9}{1}$

Q. A string vibrates with a frequency of 200 Hz. When its length is doubled and tension is altered, it begins to vibrate with a frequency of 300 Hz. The ratio of the new tension to the original tension is

Explanation

Reviewed by Dr. Abubacker

Want more practice?