Question

A 25-g string is stretched with a tension of 43 N between two fixed points 12 m apart. What is the frequency of the second harmonic?

Answer 1

The frequency of the second harmonic (
`2f_o`) is 11.97 Hz.

Step-by-step explanation:

Given;

mass of the string, m = 25 g = 0.025kg

tension on the string, T = 43 N

length of the string, L = 12 m

The speed of wave on the string is given as;

`v = \sqrt{(T)/(\mu) }`

where;

μ is mass per unit length = 0.025 / 12 = 0.002083 kg/m

`v = \sqrt{(43)/(0.002083) }\\\\v = 143.678 \ m/s`

The wavelength of the first harmonic wave is given as;

`L = (1)/(2) \lambda _o\\\\\lambda _o = 2L \\\\\lambda _o = 2 \ * \ 12\\\\\lambda _o = 24 \ m`

The frequency of the first harmonic is given as;

`f_o = (v)/(\lambda _o) = (v)/(2L) = (143.678)/(24) = 5.99 \ Hz\\\\`

The wavelength of the second harmonic wave is given as;

`L = \lambda_1 \\\\\lambda_1 = 12 \ m`

The frequency of the second harmonic is given as;

`f_1 = (v)/(\lambda _1) = (143.678)/(12) = 11.97 \ Hz = 2((v)/(\lambda _0)) = 2f_o`

Therefore, the frequency of the second harmonic (
`2f_o`) is 11.97 Hz.