Question

By what percent must one increase the tension in a guitar string to change the speed of waves on the string from 328 m/s to 363 m/s?

Please show your work and the equations you used.

Answer 1

22.47 %

Step-by-step explanation:

v 1 = 328 m/s, v 2 = 363 m/s

We know that the velocity of a wave in a stretch string is directly proportional to the square root of the tension in the string.

`(v1)/(v2)=\sqrt{(T1)/(T2)}`

`(T1)/(T2)=\left ( (328)/(363) \right )^(2)`

`(T1)/(T2)=0.8165`

Percentage increase in the tension

`(T2 - T1)/(T1)* 100 = \left ((T2)/(T1)-1  \right )* 100`

= \left ( \frac{1}{0.8165}-1 \right )\times 100

= 22.47 %