( z , t ) = A cos( kz t + ) Which of these do you prefer for a - - PowerPoint PPT Presentation

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z t a cos kz t
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( z , t ) = A cos( kz t + ) Which of these do you prefer for a - - PowerPoint PPT Presentation

Sep 15, 2023 385 likes •466 views

A "right moving" solution to the wave equation is: f R ( z , t ) = A cos( kz t + ) Which of these do you prefer for a "le fu moving" soln? A. f L ( z , t ) = A cos( kz + t + ) B. f L ( z , t ) = A cos( kz + t

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SLIDE 1

A "right moving" solution to the wave equation is:

(z, t) = A cos(kz– ωt + δ) fR

Which of these do you prefer for a "lefu moving" soln? A. B. C. D. more than one of these! E.

(z, t) = A cos(kz + ωt + δ) fL (z, t) = A cos(kz + ωt − δ) fL (z, t) = A cos(−kz– ωt + δ) fL (z, t) = A cos(−kz– ωt − δ) fL

(Assume are positive quantities)

k, ω, δ

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SLIDE 2

Two different functions and are solutions of the wave equation.

(x, t) f1 (x, t) f2 = f ∂2 ∂x2 1 c2 f ∂2 ∂t2

Is also a solution of the wave equation?

(A + B ) f1 f2

Yes, always A. No, never B. Yes, sometimes depending on and C.

f1 f2

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SLIDE 3

Two traveling waves 1 and 2 are described by the equations:

(x, t) = 2 sin(2x– t) y1 (x, t) = 4 sin(x– 0.8t) y2

All the numbers are in the appropriate SI (mks) units. Which wave has the higher speed? 1 A. 2 B. Both have the same speed C.

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SLIDE 4

Two impulse waves are approaching each other, as shown. Which picture correctly shows the total wave when the two waves are passing through each other?

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SLIDE 5

A solution to the wave equation is:

f(z, t) = A cos(kz– ωt + δ)

What is the speed of this wave? Which way is it moving? If is small (and >0), is this wave "delayed" or "advanced"? What is the frequency? The angular frequency? The wavelength? The wave number?

δ

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SLIDE 6

A solution to the wave equation is:

f(z, t) = Re [A ] ei(kz–ωt+δ)

What is the speed of this wave? Which way is it moving? If is small (and >0), is this wave "delayed" or "advanced"? What is the frequency? The angular frequency? The wavelength? The wave number?

δ

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SLIDE 7

A complex solution to the wave equation in 3D is:

(r, t) = f ˜ A ˜ei(k⋅r−ωt)

What is the speed of this wave? Which way is it moving? Why is there no ? What is the frequency? The angular frequency? The wavelength? The wave number?

δ