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Physics recheck

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Let f be the frequency, v wav the speed, and T the period of a sinusoidal traveling wave. The correct relationship is:
b)f=vwav + T

My thoughts:
Since frequency is equal to T=1/f so f=1/T. Vwav is connected to f by the equation v=lambda* frequency. so f=v/lambda. I have to connect the to f= equations inorder to get the relationship. I chose d because it seemed to combine the both.

For a transverse wave on a string the strong displacement is described as y(x,t)=f(x-at), where f is a given function and a is a positive constant. Which of the following does not necessarily follow this statement?
a)the shape of the string at time t=o is given by f(x)
b) the shape of the waveform does not change as it moves along a string
c) the waveform moves in the positive x direction
d) the speed of the waveform is a
e) the speed of the waveform is x/t

When I looked at the function equation y(x,t)=f(x-at). I thought to compare it with y(x,t)=f(kx-wt). I know that f can stand for Sin or Cos. I thought a can not be equal to the speed of the wave since v=w/k would equal it. So I chose d.

Thank you for your help. but it says that you have to connect all three .v,f, and T. I thought of that to f=1/T. How does the second question answer look. I have a question about a few other questions. If I post all my work can I get help

Why would I tell you a is the answer and all the other answers are silly? If you wnat to use d, post d. Have you considered looking at the dimension analysis of answer d? the left side is 1/sec, and the right side is m/s^2. Again, it is silly.

Your presumption of sin or cosine may be correct, but it is not stated in the problem. If the function is of x-at, then x and at have to be same units. Assume x is in meters, so at is in meters. Because t is in seconds, the a must be in meters/seconds, a velocity unit. d is correct. Your logic of choosing d however, defies my understanding.

I knew the dimensional analysis was off for the first. The question to me though sounds like they want you to include v, f, and T in your answering.

For the second one it wanted to know which of the four are not appliable to the equation. Which of the four are wrong to apply to the equation. e is right, c is right because a negative indicates a positive direction or right. From what you said it seems a is right. The only two that can be wrong then is a and b. a has to be right because f(x) indicates the function (sin or cos or another) which can dictates the shape because it indicates where the wave with start 0 or 1. So I think b must be the only one wrong.

Thank you

e is the only answer inapplicable to the question. Stop thinking sin or cosine function. Pulses, square waves, and triangular waves are quite common.

ok thank you. It just they keep using sin and cosine over and over again the chapter. So I keep thinking I can only apply that.

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