Answer to Question #195540 in Mechanics | Relativity for Mohammad Balhas

Question

Two identical waves travel in the same direction, each with a wavelength λ = 1 m and speed v = 20 m/s. When the two waves interfere, they form a resultant wave. The angular frequency of the resultant wave is:

40π rad/s

π/10 rad/s

π/5 rad/s

20π rad/s

80π rad/s

Answer 1

Gives

Wavelength $\lambda=1m$

Speedv=20m/sec

$y=Asin(wt-kx)$

Phase $\phi=(wt-kx)$

Velocity

$V=Awcos(wt-kx)$

Maximum velocity

$wt-kx=0$

cos0°=1

$w=\frac{Kx}{t}$

Put value

$w=\frac{2\pi}{\lambda }\times\frac {x}{t}$

$w=\frac{2\pi}{\lambda }\times v$

Put value

$w=\frac{2\pi}{1}\times20=40\pi Rad /sec$

Option (1) is correct