A string fastened at both ends has successive resonances with wavelengths of 0.54 m for nth harmonic and 0.48 m for the (n+1) th harmonic and 0.48 m for the (n+1) th harmonic.
(a) Which harmonics are these?
(b) What is the length of the stirng?
(c) What is the wavelength of the fundamental frequency?

Answer

A, B, C, D

Explanation

(a) `(nlambda_1)/2 = l`
`:. (n(0.54))/2 = l`
or ` n= l/ 0.27`
Similarly, `((n+1)lambda_2)/2 = l`
or ` ((n+1)(0.48))/2 = l`
or `(n+1) = l/(0.24)`
From Eqs. (i) and (ii) we have,
`n/(n+1) = 8/9`
(b) From Eq. (i),
`l= (0.27)n`
`=0.27 xx 8`
`=2.16m`
(c) `lambda/2 = l` (Fundamental)
`:. lambda = 2l = 4.32`m.