Question

The equation of stationary wave on a string clamped at both ends and vibrating in the third harmonic is given by y = 0.5 sin (0.314 x) cos (600 πt), where x and y are in cm and t in second. The length of the vibrating string is ______
(π = 3.14) 

Options

• 15 cm

• 40 cm

• 10 cm

• 30 cm

Answer 1

The equation of stationary wave on a string clamped at both ends and vibrating in the third harmonic is given by y = 0.5 sin (0.314 x) cos (600 πt), where x and y are in cm and t in second. The length of the vibrating string is 30 cm.
(π = 3.14) 

Explanation:

y = 0.5 sin (0.314 x) cos (600 πt)

0.314 x = `2pi x/lambda`

`lambda = (2pi)/3.14 = (2 xx 3.14)/(0.314)` = 20 cm

The string is vibrating in third harmonic, forming three loops.

∴ Length of string = `3. lambda/2 = (3 xx 20)/2 = 30` cm