Question

Find the first three harmonics of a string of linear mass density 2.00 g/m and length 0.600 m when the tension in it is 50.0 n.

Answer 1

As we know that Nth harmonic of the string is given by

`f = (N)/(2L)\sqrt{(T)/(m/L)}`

now here we will have

`m/L = mass density = 2 g/m`

`m/L = 0.002 kg/m`

`Length = L = 0.600 m`

`Tension = T = 50.0 N`

now from above formula we have

`f = (N)/(2(0.600))\sqrt{(50.0)/(0.002)}`

`f = 131.8N`

now for first harmonic N = 1

`f_1 = 131.8 Hz`

for second harmonic N = 2

`f_2 = 263.5 Hz`

for third harmonic N = 3

`f_3 = 395.3 Hz`