Wave motionHardBloom L3
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
Options
A.0.96 m
B.0.48 m
C.0.24 m
D.0.12 m
Solution
Sol. y = Asin (ωt – kx)
At x = 4cm, t = T/6, y = A/2
$\frac{A}{2} = A\sin\left\lbrack \frac{2\pi}{T}\left( \frac{T}{6} \right) - k\left( \frac{4}{100} \right) \right\rbrack$
sin$\left\lbrack \frac{\pi}{3} - k\left( \frac{4}{100} \right) \right\rbrack = \frac{1}{2}$
$\frac{\pi}{3} - \frac{4k}{100} = \frac{\pi}{6}$
$\frac{4k}{100} = \frac{\pi}{6}$
$k = \frac{2\pi}{\lambda} = \frac{100\pi}{24}$
$\lambda = \frac{48}{100}m = 48cm$
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