Find the speed of a transverse wave with one equation and three variables?

[ToTalk]

1. Consider a transverse wave represented by the function
y = 2.3 sin(1.9x - 25t)
where y, x, t are in meters, meters, and seconds
Determine the speed in m/s



2. No relevant equations.



3. I don't understand the way this problem is written. It seems like there are three variables with one equation, and I am supposed to arrive at a specific answer. Does anyone understand how to start this problem? Thanks very much for your help.

 

[OlderDan]

What condition must be satisfied so that y has its maximum possible value? How does the position of that maximum depend on time? What does that have to do with the velocity of the wave?

 

[ToTalk]

Hi OlderDan,

Thanks for the help! Ok, I realize that what is inside the parentheses must equal pi / 2. And does that mean that the maximum y value is 2.3? I'm still not sure about the next part.

Thanks

 

[ToTalk]

If anyone else knows how to help with this, I would appreciate the help. I think that when 1.9x - 25t = pi/2, the maximum amplitude is reached, but I am not sure how to use this info.

Thanks

 

[OlderDan]

If anyone else knows how to help with this, I would appreciate the help. I think that when 1.9x - 25t = pi/2, the maximum amplitude is reached, but I am not sure how to use this info.

Thanks

As time goes on, as it inevitably does, how does x have to change to keep 1.9x - 25t = pi/2? There is really nothing special about the value pi/2 in this question. Any constant value will do, so let's change the question to make it a bit easier. How does x have to change to keep 1.9x - 25t = 0?

 

[ToTalk]

Ok, so as t changes 1, x must change 25 / 1.9 = 13.16? So the answer is x changes 13.16 m for every 1 s change in t.

Is that correct? It seems right based on what you explained. Thanks again for all your help OlderDan.

 

[OlderDan]

Ok, so as t changes 1, x must change 25 / 1.9 = 13.16? So the answer is x changes 13.16 m for every 1 s change in t.

Is that correct? It seems right based on what you explained. Thanks again for all your help OlderDan.

That will do it. If you want to go back to the y = maximum condition where you had 1.9x - 25t = pi/2, you can solve this equation for x and graph x vs t. The graph will be a straight line with slope = Δx/Δt = 25/1.9 with an intercept of pi/(2*1.9). The intercept is the position (actually one of many positions, but you only need one) of a peak of the wave at time zero, and the graph shows the postion of that peak as a function of time. The slope Δx/Δt = 25/1.9 is the velocity of that peak, and hence the velocity of the wave.

 

[ToTalk]

Oh ok. I just did that in excel and it worked. Thanks again, that was interesting and very educational. I really gained some understanding from your help.