Traveling waves (for example, water waves or electromagnetic waves) exhibit periodic motion in both time and position. In one dimension (for example, a wave on a string), wave motion is governed by the one-dimensional wave equation below, where u(x,t) is the height or displacement of the wave surface at position x and time t, and c is the constant speed of the wave. Show that u(x.t) given below is a solution of the wave equation. u(x,t) = 2 cos (5(x+ ct)) + 7 sin (x- ct) What is the first step in showing that u(x,t) is a solution of the wave equation? O A. Factor u(x,t). du O B. Calculate the left side of the wave equation, by first calculating du YC. Calculate the left side of the wave equation, by first calculating O D. Multiply u(x,t) by c. Calculate the first partial derivative du / dt.
Traveling waves (for example, water waves or electromagnetic waves) exhibit periodic motion in both time and position. In one dimension (for example, a wave on a string), wave motion is governed by the one-dimensional wave equation below, where u(x,t) is the height or displacement of the wave surface at position x and time t, and c is the constant speed of the wave. Show that u(x.t) given below is a solution of the wave equation. u(x,t) = 2 cos (5(x+ ct)) + 7 sin (x- ct) What is the first step in showing that u(x,t) is a solution of the wave equation? O A. Factor u(x,t). du O B. Calculate the left side of the wave equation, by first calculating du YC. Calculate the left side of the wave equation, by first calculating O D. Multiply u(x,t) by c. Calculate the first partial derivative du / dt.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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traveling waves

Transcribed Image Text:Traveling waves (for example, water waves or electromagnetic waves) exhibit periodic motion in both time and position. In one dimension (for example, a wave on a
string), wave motion is governed by the one-dimensional wave equation below, where u(x,t) is the height or displacement of the wave surface at position x and time t,
and c is the constant speed of the wave. Show that u(x.t) given below is a solution of the wave equation.
Pu
u(x,t) = 2 cos (5(x+ ct)) + 7 sin (x - ct)
What is the first step in showing that u(x,t) is a solution of the wave equation?
O A. Factor u(x,t).
du
O B. Calculate the left side of the wave equation,
by first calculating
YC. Calculate the left side of the wave equation,
du
by first calculating
at
O D. Multiply u(x,t) by c.
Calculate the first partial derivative du / dt.
du
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