Question

Two identical piano wires have a fundamental frequency of 494 Hz when kept under the same tension. What fractional increase in the tension of one wire will lead to the occurrence of 5 beats/s when both wires oscillate simultaneously?

Answer 1

Answer:0.0203

Step-by-step explanation:

Given

Fundamental frequency
`\left ( f_1\right ) =494 Hz`

`\Delta f=5 beats/s`

`f_2-f_1=5`

`f_2=499 Hz`

`f_1=(1)/(2l)\sqrt{(T_1)/(\mu )}---------1`

`f_2=(1)/(2l)\sqrt{(T_2)/(\mu )}-------2`

Divide (1)&(2)

`(f_1)/(f_2)=\sqrt{(T_1)/(T_2)}`

`(T_2)/(T_1)=\left ((f_2)/(f_1) \right )^2`

`(T_2)/(T_1)-1=\left ((f_2)/(f_1) \right )^2-1`

`(T_2)/(T_1)-1=0.0203`