A. 409 Hz
The fundamental frequency of a string is given by:
where
L is the length of the wire
T is the tension in the wire
m is the mass of the wire
For the piano wire in this problem,
L = 0.400 m
T = 1070 N
m = 4.00 g = 0.004 kg
So the fundamental frequency is
B. 24
For this part, we need to analyze the different harmonics of the piano wire. The nth-harmonic of a string is given by
where is the fundamental frequency.
Here in this case
A person is capable to hear frequencies up to
So the highest harmonics that can be heard by a human can be found as follows: