The displacement of a medium in a sound wave is given by the equation `y_(1)=Acos(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.
(i) What are the wavelength and frequency of incident wave ? ________ (ii) Write the equation for the reflected wave. _________ (iii) In the resultant wave formed after reflection, find the maximum and minimum values of the particle speeds in the medium. ____________ (iv) Express the resultant wave as a superposition of a standing wave and a traveling wave. What are the positions of the antinodes of the standing wave ? What is the direction propagation of traveling wave?__________

Options

A. the frequency of the wave are `2pi//a` and `2//2pi` respectively
B. the amplitude of the reflected wave is `0.8 A`
C. the resultant wave formed after reflection is `y = A cos(ax + bt) + [-0.8 A cos(ax - bt)]` and `V_(max)` (maximum particle speed) is `1.8 bA`
D. the equation of the standing wave so formed is `y = 1.8 A sin ax cos bt`

Answer

D