Question

Find the frequencies of the first three harmonics of a 1.0-m long string which has a mass per unit length of 2.0  10–3 kg/m and a tension of 80 N when both ends are fixed in place.

Answer 1

`f_1 = 100Hz`

`f_2 = 200Hz`

`f_3 = 300Hz`

Step-by-step explanation:

Given:

Length of the string, L = 1 m

Mass per unit length, (m/L) = 2.0 × 10⁻³ kg/m

Tension in the string, T = 80N

Now, We know that,

Frequency,
`f_n= n(V)/(2L)` ................(1)

where, V = velocity

also,

`V=\sqrt{(T)/(m/L)}`

substituting the values in the equation we get

`V=\sqrt{(80N)/(2*10^(-3))}`

`V=200 m/s`

Now using the equation (1)

`f_1= (200)/(2* 1)=100 Hz`

also,

`f_2= 2* (200)/(2* 1)=200 Hz`

`f_3= 3* (200)/(2* 1)=300 Hz`

Hence, the required frequencies are

`f_1 = 100Hz`

`f_2 = 200Hz`

`f_3 = 300Hz`