Waves - peaks and zero displacement

[kenallen]

Can someone help me with this "easy" wave question?

I am given a sine wave. The snapshot shows a point of zero displacement at x=0. In terms of period of T of the wave, when will a) peak and b) the next point of zero displacement reach x=0?

the answer for a) is 3/4T and for b) is 1/2T

can someone please explain?

 

[Zorodius]

The period (T) is the amount of time it takes for the wave to pass through one complete wavelength. After one complete period, the wave will look exactly like it did when you started.

Looking at the picture you were given, can you see the point where the wave will once again look just like it does right now? The time it takes for that to happen is T, and the distance between that point and the point you started out at is $\lambda$. Now look for the point between that one and the one you started out at where the wave is at its highest point. What fraction of $\lambda$ is that? It's also that exact same fraction of T.

For part b, look for the point where the wave crosses y=0. Again, what fraction of the total wavelength is that?

 

[maverick280857]

More formally, wavelength is the minimum distance between two points on a wave that have the same phase. The time taken for this distance to be covered (at a velocity called the phase velocity of the wave) is called the time period T ($$\lambda = v_{phase}T$$). You need to determine from the figure when the shape repeats. This can be a bit tricky first but try to visualize it and after a few attempts you should be through (I think you can find a few more such questions in Resnick, Halliday and Walker Extended Edition).

Cheers
Vivek