Wave motionMediumBloom 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$\left\lbrack \frac{\pi}{3} - k\left( \frac{4}{100} \right) \right\rbrack = \frac{1}{2}$
$\frac{\pi}{3} - \frac{4k}{100} = \frac{\pi}{6}$
$\frac{4k}{100} = \frac{\pi}{6}$
$k = \frac{2\pi}{\lambda} = \frac{100\pi}{24}$
$\lambda = \frac{48}{100}m = 48cm$
Create a free account to view solution
View Solution FreeMore Wave motion Questions
A wave y = asin(ω - kx)on a string meets with another wave producing a node at x = 0. Then the equation of the unkn...Wavelenght of monochromatic light is 5000, then wave number will be :-...A uniform rope having some mass hanges vertically from a rigid support. A transverse wave pulse is produced at the lower...A wave is represented by the equation y = a sin (kx - ωt) is superimposed with another wave to form a stationary wa...In stationary wave on string :-...