Question

The displacement from the position of equilibrium of a point $4\, cm$ 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 $y=A \sin (\omega x-k x)$
$\Rightarrow \frac{A}{2}=A \sin \left(\frac{2 \pi}{T} \times \frac{T}{6}-\frac{2 \pi}{\lambda} \times 4\right)$
$\Rightarrow \frac{\pi}{6}=\frac{\pi}{3}-\frac{2 \pi}{\lambda} \times 4$
$\Rightarrow \frac{2 \pi}{\lambda} \times 4=\frac{\pi}{6}$
$\Rightarrow \lambda=48\, cm$
$\Rightarrow \lambda=0.48\, m$