The displacement of the medium in a sound wave is given by the equation `y_(1) = A cos(ax + bt)` where `A`, `a and b` are positive constants. The wave is reflected by an obstacle situated at `x = 0`. The intensity of the reflected wave is `0.64` times that of the incident wave.
(a) What are the wavelength and frequency of incident wave?
(b) Write the equation for the reflected wave.
( c ) In the resultant wave formed after reflection, find the maximum and minimum values of the particle speeds in the medium.
(d) Express the resultant wave as a superposition of a standing wave and a travelling wave. What are the positions of the antinodes of the standing wave ? What is the direction of propagation of travelling wave?

Answer

(i) `(2pi)/(a),(b)/(2pi)`
(ii) `y_(1)=-0.8 A cos (ax -bt)`
(iii) `1.8 Ab,0`
(iv) `y= - 1.6 A sin ax sin bt + 0.2 A cos (ax + bt)`
Antinodes are at `x = [n+((-1)^(n))/(2)](pi)/(a)`
Travelling wave is propagating in negative x-direction.