Acertain string on a piano is tuned to produce middle c (f = 261.63 hz) by carefully adjusting the tension in the string. for a fixed wavelength, what is the frequency when this tension is tripled?

Frequency and wavelength are two variables which are indirectly proportional.

They are related in the following equation:

f = c / w

Where,

f = frequency    c = speed of light          w = wavelength

Since c is constant, we can equate condition 1 and condition 2:

f1 w1 = f2 w2

When w2 = 3 w1, then f2 becomes:

261.63 w1 = f2 (3 w1)

Cancelling w1:

f2 = 261.63 / 3

f2 = 87.21 Hz