Waves Test - 8

As capillary & gravity waves are elastic waves or mechanical waves which require medium for their propagation.

Hence they are using the elastic behaviour of water.

Hence

The waves on the surface of water are of two kinds:

capillary waves and gravity waves

As speed of transverse & longitudinal waves depend on different modulus of elasticity (Young's modulus, Bulk modulus, Modulus of Rigidity) of the medium.

So in the same medium transverse and longitudinal waves

travel with different speeds

On comparing above equation with

y(x, t) = a sin (-kx + ωt + φ), we get

Distance traveled by wave is along - x axis

Hence y(x, t) = a sin (kx + ωt + φ) represents a wave function

travelling in the -ve x direction

In the equation

y(x, t) = a sin (kx + ωt + φ )

the term before trignometric function is called amplitude

Hence  a (term before trignometric function) is the amplitude.

In the equation 

y(x, t) = a sin (kx + ωt + φ )

the term with distance travelled 'x' is called angular wave number or propagation constant

Hence k is the angular wave number.

In the equation 

y(x, t) = a sin (kx + ωt + φ )

the term with time 't' is called angular angular velocity or angular frequency

Hence ω is the angular frequency.

In the equation

y(x, t) = a sin (kx + ωt + φ )

The term φ represents initial phase or epoch

Hence the term φ is initial phase

v is here frequency
we know that
Using Speed = distance /time
For one cycle, distance = λ , time = T
Hence V= λ /T
V=νλ

because in wave propagation particles only moves in perodic motion, particles get collide with their neighbouring particles then transfer energy to them and comes back to their normal stage. Now next particle which gain energy get into excited state and starts moving periodically and get collide to next adjacent particle and so on. Thus in wave propagation particles only transfer their kinetic energy and momentum. Hence particles does not move therefore there is no flow of matter but there is movement of disturbance.