# Problem: A piano tuner stretches a steel piano wire with a tension of 765 N. The steel wire has a length of 0.900mand a mass of 6.75 g . Part A What is the frequency f1 of the string's fundamental mode of vibration? Express your answer numerically in hertz using three significant figures. Part B What is the number n of the highest harmonic that could be heard by a person who is capable of hearing frequencies up to f = 16 kHz? Express your answer exactly.

###### FREE Expert Solution

For the fundamental mode, the required frequency is:

$\overline{){{\mathbf{f}}}_{{\mathbf{1}}}{\mathbf{=}}\frac{\mathbf{1}}{\mathbf{2}\mathbf{l}}\sqrt{\frac{\mathbf{T}\mathbf{l}}{\mathbf{m}}}}$

The highest number of harmonic, n:

$\overline{){\mathbf{n}}{\mathbf{=}}\frac{{\mathbf{f}}_{\mathbf{n}}}{{\mathbf{f}}_{\mathbf{1}}}}$

###### Problem Details

A piano tuner stretches a steel piano wire with a tension of 765 N. The steel wire has a length of 0.900mand a mass of 6.75 g .

Part A

What is the frequency f1 of the string's fundamental mode of vibration? Express your answer numerically in hertz using three significant figures.

Part B

What is the number n of the highest harmonic that could be heard by a person who is capable of hearing frequencies up to f = 16 kHz? Express your answer exactly.