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$\left\lbrack \frac{\pi}{3} - k\left( \frac{4}{100} \right) \right\rbrack = \frac{1}{2}$
$\frac{\pi}{3} - \frac{4k}{100} = \frac{\pi}{6}$
$\frac{4k}{100} = \frac{\pi}{6}$
$k = \frac{2\pi}{\lambda} = \frac{100\pi}{24}$
$\lambda = \frac{48}{100}m = 48cm$
Create a free account to view solution
View Solution FreeMore Wave motion Questions
If the velocity of sound in air is 320 m/s the frequency of the fundamental note emited by a tube of length 1m closed at...In a sound instrument fundamental freq. is 100 Hz and other resonanting frequency are 300 Hz and 500 Hz the instrument i...The wavelength of a distant star is 5700 Ao and the spectral light has a shift of 1.9 Ao towards red end then the veloci...A wave is represented by the eqn y = a sin(kx − ωt) is superimposed with another wave to form a stationary wa...A transverse wave is propagating along +x direction. At t=2 sec, the particle at x=4m is aty=2 mm.With the passage of ti...