Question

the string of a violin has a frequency of 440 cps. If the violin string is shortend by one fifth its frequency will be changed to (ans= 2200cps)

Answer 1

Answer:

$f_2=2200\:cps$

Step by step explanation:

For a violin string, we have the following formula:

$f=\frac{nc}{2l}$; where 'f' is the frequency of the wave, 'n' is the order of the harmonic, 'c' is the speed of the wave and 'l' is the length of the string.

Therefore, from this equation we deduce that the frequency is inversely proportional to the length of the string.

Therefore, $\frac{f_1}{f_2}=\frac{l_2}{l_1}$.

It is given that $f_1=440\:Hz$, and the length of the string is shortened by one fifth; i.e: $l_2=\frac{1}{5}l_1$.

It is required to find $f_2.$

Therefore,

$\frac{f_1}{f_2}=\frac{l_2}{l_1}$

$\frac{440}{f_2}=\frac{\frac{1}{5}l_1}{l_1}\\ \\ \frac{440}{f_2}=\frac{1}{5} \\ \\f_2=5*440=2200\:Hz$

Answer 2

Answer: Notice length reduced by 1/5th not reduced to 1/5th

Explanation: