Question

A transverse mechanical harmonic wave is travelling on a string. Maximum velocity and maximum acceleration of a particle on the string are 3 m/s and 90 m/s² respectively. If the wave is travelling with a speed of 20 m/s on the string. Write wave function describing the wave.

Answer 1

Given,   v_max = ωA = 3 .....(i) 

and a_max = ω²A = 90 .....(ii) 

From above equations, we have 

ω = 30 rad/s 

and A = 0.1 m 

The propagation constant,

k = ω/A = 30/20 = 1.5

Thus wave functions can be written as 

y = A sin (ωt ± kx) = 0.1 sin (30 t ± 1.5 x).