A tuning fork, frequency 388Hz, is mounted vertically on a ring stand. A string of length 2m is attached to the tuning fork, and a mass m is hung at the end of the string. The tuning fork is activated, and a wave passes through the string (wavespeed 600m/s.) Assume the tension does not affect the frequency.
If mass m is replaced with mass 4m, how many wavelengths, or fractions of a wavelength, occupy the string?
wavespeed= sqrt[tension/(mass/length)] in a vibrating string
The Attempt at a Solution
Ok, so I used the second equation to isolate T before more mass was added, assuming m=1kg. I found the tension, and it was 1800N. Then I found the wavespeed after the mass was added. Since the mass increased by a factor of 4, I used 7200N as the tension and 4kg as the mass. I found the velocity to be 60m/s. Then I used the first equation to find the wavelength, 0.15m approx. Then I divided 2 by that to find how many whole waves would occupy the string, which was 13, and apparently that is wrong.
I am not sure what I am doing wrong, thanks for helping.