A wave y = a sin(ωt − kx) on a string meets with another wave

• Oscillation Waves

A wave y = a sin(ωt − kx) on a string meets with another wave producing a node at x = 0. Then the equation of the unknown wave is

1. y = −a sin(ωt + kx)
2. y = a sin(ωt + kx)
3. y = a sin(ωt − kx)
4. y = −a sin(ωt − kx)

Answer

Equation of wave could be 

y = a sin(ωt + kx) or y = -a sin(ωt + kx)

If the given wave propagates with the upper wave, then

y = 2a cos kx sinωt

If it propagates with lower wave, then

y = -2a sin kx cosωt

Putting x = 0 in above two equations, you get

y = 2a sinωt and Y = 0

The correct option is A.