Please answer and explain these WAVES problems, thanks?

Question

1. In displacement vs. time graph, does it represent the period or the wavelength? If so, what represents the other?

2. The displacement of a string carrying travelling sinusoidal wave is given by y(x,t) = A sin (kx-wt+φ). At time t=0 the point at x=0 has a displacement of 0 and is moving in the +y direction. The phase constant φ may take the value of 180 deg. Why?

3. A source of frequency f sends waves of wavelength λ travelling with speed v in some medium. If the frequency is chaged from f to 2f, then the new wavelength and new speed will be? What is the formula/equation to use?
a. λ/2, v or b. λ, 2v

Answer 1

1. In displacement vs. time graph, the (time) period is readily measurable as the time between identical points on two successive cycles. The wavelength is derived as the wave speed (e.g., speed of light or sound) multiplied by the period; i.e., λ = VT.
2. If x is going negative at the x=0 point referred to, then y(x,t) = -A sin (kx-wt), or y(x,t) = A sin (kx-wt+φ) with φ = 180 deg. In other words adding 180 deg to a sine wave is the same as changing its sign.
3. The new speed = the old speed, since nothing was said about changing to a different medium. If the frequency doubles, there are twice as many cycles per unit distance, so the wavelength is reduced to half its previous value. Using λ = VT from (1), and the definition of frequency as F = 1/T, doubling F halves T and therefore also halves λ. I guess that's answer a.

Answer 2

1. You can find period. Period is the time taken to complete one oscillation. I don't know if you can find the wavelength or not but you can find wavelength in displacement vs distance graph by joining the point of same phase.
2. I don't know.
3. v=f(lambda) is the formula , I think.