Answer:
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;
[tex]f_o = \frac{1}{2l} \sqrt{\frac{T}{\mu} }[/tex]
where;
μ is the mass per unit length [tex]= \frac{6.0 \times 10^{-3}}{0.8} = 7.5 \times 10^{-3} \ kg/m[/tex]
[tex]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[/tex]
Therefore, the frequency of the fundamental mode of vibration is 199.6 Hz
