Question

Identical cellos are being tested. One is producing a fundamental frequency of 130.9Hz on a string that is 1.25m long and has a mass of 109g. on the second cello the same string is fingered to reduce the length that can vibrate. if the beat frequency produced by these two strings is 4.33Hz, what is the vibrating length of the second string?

Answer 1

Answer:

the vibrating length of the second string $L_2= 1.209 m$

Explanation:

Formula for fundamental frequency is

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

from this equation we can say that

frequency is inversely proportional to the length of string

⇒$\frac{L_2}{L_1}=\frac{f_1}{f_2} }$.........................1

Here $L_1= 1.25 m$

$f_1= 130.9 Hz$

$f_2-f_1= 4.33Hz$

⇒$f_2= 4.33+130.9= 315.23 Hz$

now putting values in equation 1 we get

$\frac{L_2}{1.25}=\frac{130.9}{135.23} }$.

$L_2= 1.209 m$