First slide

Characterstics of wave

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 = $\frac{T}{6}$ (T is the time period). Assume that the source was at mean position at t = 0. The wavelength of the running wave is:

Moderate

A

0.96 m
B

0.48 m
C

0.24 m
D

0.12 m

Solution

Equation of wave is y = A sin $(ωt - kx)$
$\Rightarrow \frac{A}{2} = Asin (\frac{2 π}{T} \times \frac{T}{6} - \frac{2 π}{λ} \times 4)$
$\Rightarrow \frac{π}{6} = \frac{π}{3} - \frac{2 π}{λ} \times 4 \Rightarrow \frac{2 π}{λ} \times 4 = \frac{π}{6}$
$\Rightarrow λ = 48 cm$
$\Rightarrow λ = 0.48 m$

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