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A string lies along the x axis, and is tied at its ends at x = ±. The string is vibrating, and its displacement f satisfies the wave equation: a² f əx² = 1 0² f c² Ət² Show that f(x, t) = sin(ct) sin(x) satisfies the wave equation. Also show that the displace- ment is zero at the endpoints x = ± for all time t.

A string lies along the x axis, and is tied at its ends at x = ±. The string is vibrating, and its displacement f satisfies the wave equation: a² f əx² = 1 0² f c² Ət² Show that f(x, t) = sin(ct) sin(x) satisfies the wave equation. Also show that the displace- ment is zero at the endpoints x = ± for all time t.

Advanced Engineering Mathematics
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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3. A string lies along the x axis, and is tied at its ends at x = ±. The string is vibrating, and its displacement f satisfies the wave equation: a² f ?x2 - 1 0² f c² Ət² Show that f(x, t) = sin(ct) sin(x) satisfies the wave equation. Also show that the displace- ment is zero at the endpoints x = ±7 for all time t.
Transcribed Image Text:3. A string lies along the x axis, and is tied at its ends at x = ±. The string is vibrating, and its displacement f satisfies the wave equation: a² f ?x2 - 1 0² f c² Ət² Show that f(x, t) = sin(ct) sin(x) satisfies the wave equation. Also show that the displace- ment is zero at the endpoints x = ±7 for all time t.
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