Homework for Basic Language of Waves

1. (a) for A = 1 unit; $k$ = 2$\pi$ m$^{-1}$; $\omega = \pi $ rad/s. What are the wavelength, period and amplitude of the disturbance? Discuss the dimensions of A.

(b) Plot in Mathematica two spatial cycles of the waveform and animate for two time periods.

( c ) Which direction does the wave travel and with what speed? Which direction does it travel if you change the sign of the position term? Of the time term? Of both? Why?

(d) Focus on the position $x$ = 0 m. At what rate is the quantity represented by $\psi$ changing at $t$ = 0, ¼,1/2, and 1s? Describe the variation over one cycle.

2. Write down & plot in Mathematica a sinusoidal waveform $\psi$(x,t) that has the following properties: (a) Amplitude 2 m, wavelength 10 m, travels to the right at 1 m/s, $\psi$ = 2 m at $x$ = 5m and $t$ = 0 s.

(b) Standing wave, amplitude 5 m, period 1 s, wavelength 1 m that is momentarily flat at $t$ = 0 s.

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