Question

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

Answer 1

the frequency of the fundamental mode of vibration is 199.6 Hz

Step-by-step 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 = (1)/(2l) \sqrt{(T)/(\mu) }`

where;

μ is the mass per unit length
`= (6.0 * 10^(-3))/(0.8) = 7.5 * 10^(-3) \ kg/m`

`f_o = (1)/(2l) \sqrt{(T)/(\mu) } \\\\f_o = (1)/(2* 0.8) \sqrt{(765)/(7.5 * 10^(-3)) } \\\\f_o = 199.6 \ Hz`

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