Physics: A piano tuner stretches a steel piano wire with a tension of 765 N. The steel wire has a length of 0.800 m and a mass of 6.00 g . What is the frequency f1 of the string s fundamental mode of vibration

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A piano tuner stretches a steel piano wire with

ynclankaedon

15.05.2021

the frequency of the fundamental mode of vibration is 199.6 Hz

Explanation:

Given;

tension of the piano wire, T = 765 N

length of the steel wire, L = 0.8 m

mass of the steel wire, m = 6.00 g = 6 x 10⁻³ kg

The frequency of the fundamental mode of vibration is calculated as;

$f_o = \frac{1}{2l} \sqrt{\frac{T}{\mu} }$

where;

μ is the mass per unit length $= \frac{6.0 \times 10^{-3}}{0.8} = 7.5 \times 10^{-3} \ kg/m$

$f_o = \frac{1}{2l} \sqrt{\frac{T}{\mu} } \\\\f_o = \frac{1}{2\times 0.8} \sqrt{\frac{765}{7.5 \times 10^{-3}} } \\\\f_o = 199.6 \ Hz$

Therefore, the frequency of the fundamental mode of vibration is 199.6 Hz

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