Two traveling sinusoidal waves are describe by the wave function y_1 = (5.00 m)s
ID: 1517593 • Letter: T
Question
Two traveling sinusoidal waves are describe by the wave function y_1 = (5.00 m)sin[(pi 400x - 1200t)] and y_2 = (5.00 m)sin [pi (4.00x - 1200t - 0.250)] Where x, y_1, and y_2 are in meters and t is in seconds, (a) What is the amplitude of the resultant wave? (b) What is the frequency of the resultant wave? Question one: 9.24 600 Hz Question two: 4.24 cm 6 cm -6 cm 1/2, 3/2, 5/2 Two sinusoidal waves combining in a medium are described by the wave functions y_1 = (3.0cm)sin pi (x + 0 60t) and y_2 = (3.0cm)sin pi(x - 0.60t) Where x is in centimeters and t is in seconds Determine the maximum transverse position of an element of the medium at (a) x = 0.250 cm. (b) x 0 500 cm, and (c) x = 1.50 cm. (d) Find the three smallest values of x corresponding to antinodes. Two speakers are driven by a common oscillator at 800 Hz and face each other at a distance of 1.25 m. Locale the points along a line joining the two speakers where relative minima would be expected (use v = 343 m/s). At 0.0891 m, 0.303 m, 0.158 m. 0.732 m. 0.947 m, and 1.16 m from one speaker. A sinusoidal wave is described by the equation y_1 = (0 080 m) sin (2pi(0 100x - 80 0 t)] Where y_1 and x are in meters and t is in seconds Write an expression for a wave that has the same frequency, amplitude, and wavelength as y_1 but which, when added to y_1, gives a resultant with an amplitude of 8sqrt3 cm. (0.0800 m)sin(2pi(0.100 x -80 0 t +0.167)Explanation / Answer
1) You can use the trig identity sin u + sin v = 2 sin(½(u+v)) cos(½(uv)) with u=4.00x - 1200t and v=4.00x - 1200t - 0.25. You should find that the resultant wave is given by 2*(5m)* sin(4x-1200t-.25) *cos(.25). That means:
a) The amplitude is 2*(5.0m)*cos(.25) =9.99m
b)(1200 x Pi) / (2 x Pi) => = 1200/2 = 600 Hz
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