Apiano tuner stretches a steel piano wire with a tension of 1070 n . the wire is 0.400 m long and has a mass of 4.00 g . a. what is the frequency of its fundamental mode of vibration?
b. what is the number of the highest harmonic that could be heard by a person who is capable of hearing frequencies up to 1.00×10^4 hz ?

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:

number of electrons for neutral cl