#$&*
Phy 242
Your 'question form' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
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I'm working on Test 2 and have a few questions:
1) Show that the function y(x,t) = 0.6e^-(920t-0.9x)^2 satisfies the wave equation, and give the freq, wavelength, and vel of wave. Sketch wave from x = -5 to 5 and t = 0 to 0.002178.
@& The wave equation is a partial differential equation that relates y_xx to y_tt.
You can easily enough find y_xx and y_tt, and you should do so.
Then look up the wave equation and see if your derivatives fit it.
If t = 0, what is the function? Describe the resulting graph of y vs. x, and graph it from t = -5 to t = 5.
Then repeat for t = .002178 (or just round to .0022). Describe this result.*@
2)Two sources separated by 9.75 m emit waves with wavelength 1.45m with the waves in phase. The waves travel at identical velocities to a distant observer. At any point along the perp bisector of the line segment connecting the two points, the two waves will arrive in phase an hence reinforce. What are the first 3 nonzero angles with the perp bisector at which the first interference minimum will be observed?
@& A and B refer to the positions of the two sources.
The direction of the perpendicular bisector of the line segment AB is that of normal vector normal to AB.
If the paths from points A and B both make angle theta with the normal vector, then what is the path difference?
What path differences will result in positive reinforcement? What path differences will result in negative reinforcement?
What angles will result in the desired path differences?
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3)If hearing threshold intensity is 10^-12 watts/m^2, then what is the intensity of a sound which meausres 31 decibals?
@& What is the definition of the decibel intensity of a given sound?
How can you use this definition to solve the given problem?*@
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1) I know that y(x,t) = A sin (kx) sin (omega*t) and y(x,t) = A sin (pi/L * x) sin (v/2L * t). But, would I plug in x = 5 for x and t = 0.002178 for t in the second equation? Where would I get L from?
@& You're thinking in terms of a standing wave. The given equation is for a traveling wave, so L is not relevant.
The wavelength, frequency and wave speed are relevant, and are directly related to the coefficients of x and t in the given equation.*@
2)I can't follow this question really good. I'm sure it's probably simple but can you get me started on it?
3)I think I know this one, but I just wanted to make sure before I study it. 31 = 10 * log (intensity/10^-12), then solve for intensity?!
@& Rght.*@
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@& I've inserted some guideline questions under the problem statements, and some additional notes under your later comments.
Feel free to submit any of these problems again, with additional information, if you have additional questions.*@