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Express your answers for (a)-(d) in terms of A, k, and o for the first four parts. (a) In what direction is the wave traveling? (b) Find the speed of transverse waves, vp, on this string (c) Find the y-velocity, v,(x,t), of a point on the string as a function of x and t. (d) Find the slope of the string, oy(x, t)/ox, as a function of the position x and the time t. What is the ratio of the slope of the string to the y-velocity of part (c)?

Express your answers for (a)-(d) in terms of A, k, and o for the first four parts. (a) In what direction is the wave traveling? (b) Find the speed of transverse waves, vp, on this string (c) Find the y-velocity, v,(x,t), of a point on the string as a function of x and t. (d) Find the slope of the string, oy(x, t)/ox, as a function of the position x and the time t. What is the ratio of the slope of the string to the y-velocity of part (c)?

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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Traveling and standing waves First consider a transverse wave traveling in a string. The mathematical form of the wave is y(x, t) = A cos(-k x+ wt). Express your answers for (a)-(d) in terms of A, k, and o for the first four parts. (a) In what direction is the wave traveling? (b) Find the speed of transverse waves, vp, on this string (c) Find the y-velocity, v,(x,t), of a point on the string as a function of x and t. (d) Find the slope of the string, ôy(x, t)/ôx, as a function of the position x and the time t. What is the ratio of the slope of the string to the y-velocity of part (c)?
Transcribed Image Text:Traveling and standing waves First consider a transverse wave traveling in a string. The mathematical form of the wave is y(x, t) = A cos(-k x+ wt). Express your answers for (a)-(d) in terms of A, k, and o for the first four parts. (a) In what direction is the wave traveling? (b) Find the speed of transverse waves, vp, on this string (c) Find the y-velocity, v,(x,t), of a point on the string as a function of x and t. (d) Find the slope of the string, ôy(x, t)/ôx, as a function of the position x and the time t. What is the ratio of the slope of the string to the y-velocity of part (c)?
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