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.

Respuesta :

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.

[tex]\frac{v1}{v2}=\sqrt{\frac{T1}{T2}}[/tex]

[tex]\frac{T1}{T2}=\left ( \frac{328}{363} \right )^{2}[/tex]

[tex]\frac{T1}{T2}=0.8165[/tex]

Percentage increase in the tension

[tex]\frac{T2 - T1}{T1}\times 100 = \left (\frac{T2}{T1}-1  \right )\times 100[/tex]

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

                                                 = 22.47 %