Equation of a wave travelling in a medium is: `y=a sin (bt-cx)`. Which of the following are correct?

Options

A. Ratio of the displacement amplitude, eith which the particles of the medium oscillate, to the wavelength is equal to `ac//2pi`
B. Ratio of the velocity oscillation amplitude of medium particles to the wave propagation velocity is equal to `ac`
C. oscillation amplitude of relative deformation of the medium is directly proportional to velocity oscillation amplitude of medium particles
D. non of the above

Answer

a., b., c.

Explanation

Comparing the given equation of travelling wave with
`y=a sin (omegat-(2pix)/(lambda))`
Amplitude=a, angular frequency `omega=b and 2pi//lambda=c` or wavelength `lambda=2pi//c`
`(a)/(lambda)=(ac)/(2pi)`
Therefore, option (a) is correct.
Velocity oscillation amplitude of medium particles is `aomega=ab`.
wave propagation velocity `v=omegalambda//2pi=b//c`
`(aomega)/(v)=ac`
Hence, option (b) is also correct.
Relative deformation or strain produced in the medium is `epsilon=mu//v`, where `mu` is particle's velocity and 'v' is wave velocity. since `v` is property of the medium, therefore, `epsilon` is derectly propagation to velocity of the medium particle `(u)`.
`epsilon` will be maximum possible when `u` is maximum. hence, option (c ) is also correct.