Question

To see how two traveling waves of the same frequency create a standing wave.
Consider a traveling wave described by the formula
y1(x,t)=Asin(kx−ωt).
This function might represent the lateral displacement of a string, a local electric field, the position of the surface of a body of water, or any of a number of other physical manifestations of waves.

At certain times, the string will be perfectly straight. Find the first time t1>0 when this is true.
Express t1 in terms of ω, k, and necessary constants.

The answer is t1=pi/2ω

can you please explain how this came to be? thanks

Answer 1

The equation of standing wave is y(x,t)=(2Asinkx)cosωt.
The string can be straight only when cosωt =0, for then y(x,t)=0 also (for all ‘x’)
If cosωt₁ =0, ωt₁=π/2, => t₁=π/2ω