Question

The displacement of the medium in a sound wave is given by the equation $y_1=Acos(ax+bt)$ where ,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. Then, the wavelength ond frequency of the incident wave are

• A. $a,b$
• B. $2\pi a,2\pi b$
• C. $2\pi /a,2\pi /b$
• D. $2\pi /a,b/2\pi$

Answer 1

The correct option is D $2\pi /a,b/2\pi$

Displacement equation of wave is given by $y=Acos(kx+wt)$ .........(1)

Compairing (1) with $y_1=Acos(ax+bt)$

Thus $a=k=\frac{2\pi }{\lambda }$ where $\lambda$ is the

wavelength of the wave.

$⟹\lambda =\frac{2\pi }{a}$

Also $b=w=2\pi \nu$ where $\nu$ is the frequency of wave.

$⟹\nu =\frac{b}{2\pi }$