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. a²u at² a²u dx² = ². u(x,t) = 4 cos (5(x + ct)) + 3 sin (x- ct) What is the first step in showing that u(x,t) is a solution of the wave equation? a²u first calculating [2 O A. Calculate the left side of the wave equation, OB. Factor u(x,t). O c. Calculate the left side of the wave equation, O D. Multiply u(x,t) by c². a²u 21² first calculating ди ət ди ax
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. a²u at² a²u dx² = ². u(x,t) = 4 cos (5(x + ct)) + 3 sin (x- ct) What is the first step in showing that u(x,t) is a solution of the wave equation? a²u first calculating [2 O A. Calculate the left side of the wave equation, OB. Factor u(x,t). O c. Calculate the left side of the wave equation, O D. Multiply u(x,t) by c². a²u 21² first calculating ди ət ди ax
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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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 and c is the constant speed of the wave. Show that u(x,t) given below is a solution of the wave equation.
a²u
at²
a²u
= = c2
dx²²
u(x,t) = 4 cos (5(x + ct)) + 3 sin (x - ct)
What is the first step in showing that u(x,t) is a solution of the wave equation?
O A. Calculate the left side of the wave equation,
B. Factor u(x,t).
C. Calculate the left side of the wave equation,
O D. Multiply u(x,t) by c².
a²u
at²
a²u
at²
by first calculating
by first calculating
ди
at
ди
ox.
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