Vibrations and tension?

Question

I'm not too sure how to approach this question:

A string is supposed to vibrate at 200 Hz. It actually vibrates at 205 Hz. What percent should the tension in the string be changed to correct the frequency?

Thanks.

Answer 1

A string fixed at both ends vibrates at f = nc/(2L)

f=frequency
c= speed of a transverse wave along the string
L=length of the string
n=1,2,3... (use 1 here for the fundamental frequency.)

The speed of a transverse wave along a wire is c = (T/u)^(1/2)

T=tension
u=mass/length of the string.

If you substitute the expression for c into the expression for f, you see that the frequency is proportional to the square root of the tension of the string.