write the wave functions for traveling waves with these characteristics given different initial conditions
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Consider $\quad$ two $\quad$ wave $\quad$ functions $$y_{1}(x, t)=4.00 \mathrm{m} \sin \left(\pi \mathrm{m}^{-1} x-\pi \mathrm{s}^{-1} t\right)$$,and $$y_{2}(x, t)=4.00 \mathrm{m} \sin \left(\pi \mathrm{m}^{-1} x-\pi \mathrm{s}^{-1} t+\frac{\pi}{3}\right)$$.(a) Using a spreadsheet, plot the two wave functions and the wave that results from the superposition of the two wave functions as a function of position $(0.00 \leq x \leq 6.00 \mathrm{m})$ for the time $t=0.00 \mathrm{s} .$ (b) What are the wavelength and amplitude of the two original waves? (c) What are the wavelength and amplitude of the resulting wave?
SITUATION 5: Shown below is the plot of a wave function that models a wave at time t = 0.00s and t = 2.00s. Take crests of the dotted line and solid line at 0.25m and 0.9m, respectively. a. Determine the amplitude and wave number of the wave. b. Calculate the wave speed and angular frequency of the wave. c. Write the wave function of the wave. d. If the dotted and solid waves travel in the opposite direction, write the wave function of the resulting standing wave. y(m) = 0.40 0.30 0.20 0.10 0.00 x(m) = 0.10 -0.20 0.30 0.40 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
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