Question

The displacement of the medium in a sound wave is given by the equation; $y_1=Acos(ax+bt)$ where A, a & 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. The wavelength of the incident wave is $\frac{x\pi }{a}$. Find the value of $x$ :

Answer 1

Wavelength of the incident wave $\lambda =\frac{x\pi }{a}$ .

Displacement equation of a given incident wave $y_1=Acos(ax+bt)$

On comparing with $y=Acos(kx+wt)$ we get $a=k$

Thus $a=\frac{2\pi }{\lambda }$

$a=\frac{2\pi }{\frac{x\pi }{a}}⟹x=2$