Question

The displacement from the position of equilibrium of a point $4cm$ from a source of sinusoidal oscillations is half the amplitude at the moment $t=T/6(T$ is the time period). Assume that the source was at mean position at $t=0$. The wavelength of the running wave is:

• A. 0.96 m
• B. 0.48 m
• C. 0.24 m
• D. 0.12 m

Answer 1

Answer: (B)

Equation of wave is $y=A\sin (\omega x-kx)$
$\Rightarrow \frac{A}{2}=A\sin \left(\frac{2\pi }{T}\times \frac{T}{6}-\frac{2\pi }{\lambda }\times 4\right)$
$\Rightarrow \frac{\pi }{6}=\frac{\pi }{3}-\frac{2\pi }{\lambda }\times 4$
$\Rightarrow \frac{2\pi }{\lambda }\times 4=\frac{\pi }{6}$
$\Rightarrow \lambda =48cm$
$\Rightarrow \lambda =0.48m$