Question

Equation of a transverse wave travelling in a rope is given by y = 5 sin(4t - 0.02x) where y and x are expressed in cm and time in seconds. Calculate

(a) the amplitude frequency, velocity and wavelength of the wave.

(b) the maximum transverse speed and acceleration of a particle in the rope.

Answer 1

(a) Comparing this with the standard equation of wave motion

where A, f and λ are amplitude, frequency and wavelength respectively. 

Thus, amplitude

Maximum velocity of the particle = 20 cm/s

Particle acceleration 

Maximum particle acceleration = 80 cm/s²