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

Answer:

22.47 %

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.

$\frac{v1}{v2}=\sqrt{\frac{T1}{T2}}$

$\frac{T1}{T2}=\left ( \frac{328}{363} \right )^{2}$

$\frac{T1}{T2}=0.8165$

Percentage increase in the tension

$\frac{T2 - T1}{T1}\times 100 = \left (\frac{T2}{T1}-1 \right )\times 100$

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

                                                 = 22.47 %