Question

Two particles of a medium disturbed by the wave propagtion are at `x_(1)=0` and `x_(2)=1` cm The wave is propagating in positive x-direction The displacement of the particles is given by the equation: `y_(1)=(2sin3pit)` cm and `y_(2)=2sin(3pit-pi//8)` cm (t is in seconds)
A. The frequency of wave is `1.5` Hz
B. Wavelength of the wave can be 16 cm
C. Velocity of the wave can be 24 cm//s
D. Wave equation can be `y=(2)sin[(2pi)/16(24t-x)]` cm.

Answer 1

Correct Answer - A::B::C::D
As the motions of particles are simple harmonic, amplitude =2 cm
`omega` (Angular frequency) `=3pirad//sec`
As the phase difference of particles separated by 1 cm is `pi//8`
`lambda=8/pixx2pi=16` cm
Hence, wave velocity `=omega/(2pi)xxlambda=24` cm//s
`y=(2)sin[(2pi)/16(24t-x)]` cm