Frequency on Waves and Tension Quick Question

[isisfierce]

1. Two piano strings are supposed to be vibrating at 128 Hz, but a piano tuner hear three beats every 2 seconds when they're played together

a) If one is vibrating at 128 Hz, what must be the difference between their frequencies?
Answer - 3 Beats Per Two Seconds, Frequency Diff = 1.5

b) By how much in percent must the tension be increased or decreased to bring them in tune?

-- B is where I'm stuck on. I have the two equations v= lambda x frequency and
velocity = sqrt ( Tension / mass per length )

So I set both of them equal to each other and found that the Tension is proportional to the Frequency Squared?? I'm not sure if this is the right direction :( And if it is I tried putting in the number percent but it didn't work ( Sqrt 1.5 )

 

[isisfierce]

=] Bump!

 

[isisfierce]

another bump!

 

[nasu]

You have standing waves in the string. The wavelength is determined by the length of the string.
L= n (lambda/2) if it's fixed at both ends.

lambda= v/f and use v=sqrt(T/linear density)

solve these to get frequency as a function of T .

You know the relative change in frequency (1.5/128) so you can calculate the relative change in tension.

 

[merryjman]

There is an equation that shows how the "beat" frequencies occur. If you've got two sine waves, sin(A) and sin(B), and A is different from B, there's a trig identity that allows you to add them together and find sin(A + B). If you know the beat frequency and A, you can find B.