Question

We want to tune the second string of a guitar to its standard frequency of 245 Hz. We listen to the beats

produced when the string is played at the same time as a tuning fork.

(a) If we hear 6 beats/s, should the tension in the string be increased or decreased? Explain.

(b) We decrease the tension and the beating increases to 10 beats/s. Should we tighten or loosen the string?

(c) Starting from 10 beats/s, by what percentage must the tension be changed in order to tune the string?

Answer 1

In order to not hear any beats, the tuning fork should be tuned to the desired frequency of 245 Hz of guitar and then loosen or tighten the string of the guitar so as to match with the tuning fork frequency of 245 Hz.

(a) As we hear to beats of 6 beats/second, |fg-ft| = 6

Frequency is proportional to the tension in the string.

|fg-245| = 6

fg = 251 Hz or 239 Hz

Tension can be either decreased or increased.

(b) Now the tension in the string is reduced (fg is reduced) which increases the beats to 10. It indicates that we are drifting down from 245 Hz, we should increase the tension or tighten the string.

(c) f is proportional to the square root of T,

Now the fg is 235 Hz, we need it to make 245 Hz

245/235 = sqrt(Tnew/Told)

Tnew = 1.0869 Told

% change = Tnew - Told/Told *100 = 8.69% the tension in the string should be increased (changed) to tune the string.