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notka56 [123]
3 years ago
15

A piano tuner stretches a steel piano wire with a tension of 765 N . The steel wire has a length of 0.600 m and a mass of 4.50g

.
What is the frequency (f_1) of the string's fundamental mode of vibration?
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?
Physics
1 answer:
Inga [223]3 years ago
6 0

Answer:

266.14532 Hz

60

Explanation:

m = Mass of string = 4.5 g

T = Tension = 765 N

L = Length of string = 0.6 m

f = Frequency = 16 kHz

Linear density is given by

\mu=\dfrac{m}{L}\\\Rightarrow \mu=\dfrac{4.5\times 10^{-3}}{0.6}\\\Rightarrow \mu=0.0075\ kg/m

Fundamental frequency is given by

f'=\dfrac{1}{2L}\sqrt{\dfrac{T}{\mu}}\\\Rightarrow f'=\dfrac{1}{2\times 0.6}\sqrt{\dfrac{765}{0.0075}}\\\Rightarrow f'=266.14532\ Hz

The fundamental frequency is 266.14532 Hz

The number of loops is given by

n=\dfrac{f}{f'}\\\Rightarrow n=\dfrac{16000}{266.14532}\\\Rightarrow n=60.11753

The number of loops is 60.

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