Question

The equation of vibration of a stretched string fixed at both ends and vibrating in 5^th harmonic is Y = 3 sin(0.4x) cos(200πt) where 'x' and 'Y' are in cm and t in second. The length of the string is ______

Options

• (12.5) π cm

• (10.5) π cm

• (8.5) π cm

• (4.5) π cm

Answer 1

The equation of vibration of a stretched string fixed at both ends and vibrating in 5^th harmonic is Y = 3 sin(0.4x) cos(200πt) where 'x' and 'Y' are in cm and t in second. The length of the string is (12.5) π cm.

Explanation:

For the 5^th harmonic, the string of length L vibrates in 5 loops

`(5lambda)/2 = L`

Now `(2pi)/lambda = 0.4`

∴ `lambda = (2pi)/0.4 = (20pi)/4 = 5pi`

∴ L = `(5 xx 5pi)/2 = (25pi)/2 = 12.5 pi`