Question

#4

3. Demonstrate that the following equations satisfy the "wave equation." For those that do, find the wave amplitude, wave speed, wavenumber, wavelength, angular frequency, and frequency in Hz? Also, denote if the wave is rightward or leftward travelling. c. y(x,t) 6cos(3x+18t) d. y(x,t) -3tan(6x+60t) yx,t) -6cos(67x)cos(80t) e. 4. For the equation given in 3(a), plot the response using a PC as a function of x over at least two full wavelengths at r-0.1 second. On a different plot, show the response at the point x-0.1 m as a function of time for at least two full cycles.

Answer 1

Harmonic forms Harmonic forms comprise one useful subset of shapes. These include the following: t y(x,t) A Sin[27 + 4] -) t y(x,t) ACos[27 + ] T y(x,t)- A Exp[27i T t x y(x,t) A Exp[-2n i T where A is the wave amplitude, x is the spatial position, t is the time, lambda is the wavelength, Tis the wave period, and phi is an initial phase.

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(8oft) NM,) 6Co (67n) Co 1 (6nnt8on) Cor Gn (F) 2 Co ont)+ 9Ccs(6n2-8i+. Amplituol A26 &A d 2 80六 7 Yo. fitive dliacti diactiy t GCont8t). toLu ReetColou C4Cos(3a +18+> black Colon

6Cos16) Cos (8ot blue Colo tz01de a0jautAGrieCo one

10 (0.6, 6) 4 0 2 |(1.647, -6) -10

10 (0.3657, 6) b.5 0 (0.1912, -6) --10

10 (0.1667, 6) 0!5 00 1 (0.3333, -6) --10

(0, 1.854) (0.03125, 0) 0.05 0.1 0 (0.0125, 1.854)