The wave functions of two standing waves on a string of length L are y 1 (x, t) A 1 cos 1 t sin k 1 x and y 2 (x, t) A 2 cos 2 t sin k 2 x, where k n n L, and n nw 1 The wave function of the resultant wave is y r (x, t) y 1 (x, t) y 2 (x, t) (a) Find the velocity of a segment dx of the string (b) F...

a v y y r t 1 A 1 sin 1 tsin k 1 x 2 A 2 sin 2 tsin k 2 x b dK 12v y 2 dx 12 ...

The wave functions of two standing waves on a string of length L are y 1 (x,

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The wave functions of two standing waves on a string of length L are

y₁(x, t) = A₁ cos ώ₁t sin k₁x

and

y₂(x, t) = A₂ cos ώ₂t sin k₂x,

where k_n = nπ/L, and ώ_n = nw₁. The wave function of the resultant wave is

y_r(x, t) = y₁(x, t) + y₂(x, t).

(a) Find the velocity of a segment dx of the string.

(b) Find the kinetic energy of this segment.

(c) By integration, find the total kinetic energy of the resultant wave. Notice the disappearance of the cross terms so that the total kinetic energy is proportional to (n₁A₁)²+ (n₂A₂)².

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Fundamentals of Ethics for Scientists and Engineers

ISBN: 978-0195134889

1st Edition

Authors: Edmund G. Seebauer, Robert L. Barry

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Question Posted: Jul 14, 2011 08:08 PM

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The wave functions of two standing waves on a string of length L are y 1 (x,

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Fundamentals of Ethics for Scientists and Engineers

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