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# Lec4 - a period except that the period is shifted by an...

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a period, except that the period is shifted by an amount of kx , and therefore the integral is not changed because of it. Therefore, dk dt = 1 2 μv ω 2 y 2 m cos 2 ( kx - ω t ) = 1 4 μv ω 2 y 2 m We won’t show this here, but dP dt = dK dt so that dE dt = 1 2 μv ω 2 y 2 m Exercise : Find the above average by averaging over a wavelength (instead of averaging over a period). Change of linear mass density Usually the frequency f is determined by the external force. As the speed depends only on the “hardware,” not on the frequency, then λ = v f implies that increasing f results in a smaller λ . Consider a string with two parts: one with linear mass density μ 1 and the other with μ 2 . How is the wave changing? Assume that the wave propagates initially in the medium μ 1 . It is the local physics that determines the speed. Therefore, v 1 = τ μ 1 , v 2 = τ μ 2 . What about the interface? Continuity of the string requires that the string moves the same way on either side of the interface, i.e., the amplitude is unchanged ( f is also the same from the requirement of continuity at the interface; also, it is required by conservation of energy).

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Lec4 - a period except that the period is shifted by an...

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