Question

The percent by which the fundamental frequency changed if the tension is increased by 30 percent is ? a)-20.04% b)-40.12% c)-30% d)-14.02%

Answer 1

Answer:

Percentage increase in the fundamental frequency is

d)-14.02%

Explanation:

As we know that fundamental frequency of the wave in string is given as

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

now it is given that tension is increased by 30%

so here we will have

$T' = T(1 + 0.30)$

$T' = 1.30T$

now new value of fundamental frequency is given as

$f_o' = \frac{1}{2L}\sqrt{\frac{1.30T}{\mu}}$

now we have

$f_o' = \sqrt{1.3}f_o$

so here percentage change in the fundamental frequency is given as

$change = \frac{f_o' - f_o}{f_o} \times 100$

% change = 14.02%