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Harmonics of a Piano

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Harmonics of a Piano Wire

A piano tuner stretches a steel piano wire with a tension of 800 N. The steel wire has a length of 0.400 m and a mass of 3.00 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.

So f1 = _______________ Hz

Hints:

Harmonics of a Piano Wire
What is the frequency of the string's fundamental mode of vibration?

Hint 1. How to approach the problem

Find the mass per unit length for the wire. Then apply the equation for the fundamental frequency of the wire.

Hint 2. Find the mass per unit length

What is the mass per unit length for the wire?
Express your answer numerically in kilograms per meter using three significant figures.
=

Hint 3

This hint will be visible after you complete previous item(s). (will send this hint if needed after previous items are answered)

Part B:

What is the number of the highest harmonic that could be heard by a person who is capable of hearing frequencies up to 10,000 Hz?

n = ___________

Part B Hints:

Harmonics of a Piano Wire
What is the number of the highest harmonic that could be heard by a person who is capable of hearing frequencies up to 10,000 Hz?

Hint 1. Harmonics of a string

The harmonics of a string are given by fn=nf1, where fn is the nth harmonic of a string with fundamental frequency f1. Be careful if you get a noninteger answer for n, as harmonics can only be integer multiples of the fundamental frequency.
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