Question

Suppose a piano tuner hears 3 beats per sec-
ond when listening to the combined sound
from his tuning fork and the piano note being
tuned. After slightly tightening the string, he
hears 5 beats per second.
Should the string be loosened or tightened?
1. The string should be tightened because
the frequency of the string is 5 Hz below the
correct freguency.
2. The string should be tightened because
the frequency of the string is 5 Hz above the
correct frequency.
3. The string should be loosened because
the frequency of the string is 5 Hz above the
correct frequency.
4. The string should be loosened because
the frequency of the string is 5 Hz below the
correct frequency.
5. The string should be loosen to increase its
frequency.

Answer 1

Answer: 3 The string should be loosened because  the frequency of the string is 5 Hz above the  correct frequency.

Explanation:  In order to explain this problem we have to consider the relationship bewteen the Tension and the frequency, this is given by:

We know that:

$v=\sqrt{T/\mu$ where μ and T are the mass linear density and Tension of teh string, respectively.

We also know that v=λ*ν the speed is related to the wavelength (λ) and the frequency (ν).

Then we have that frequency depents  directely of the Tension (T) on the string.

In our case the frequency to be tuned is 3 Hz, firstly the piano tuner slightly tightening then he  hears 5 beats per second (5 Hz). Then it is neccesary loose the tension on the string because the actual frequency is above to the correct frequency (3 Hz).