The questions states; A 524 Hz longitudinal wave in air has a speed of 345 m/s W

Question

The questions states; A 524 Hz longitudinal wave in air has a speed of 345 m/s Write the equation for this wave traveling to the right, if its amplitude is 0.020 cm, and D = - 0.020 cm, at t = 0 and x = 0. Express your answer in terms of the variables x, t, and appropriate constants. So my method for this was to set 2 pi x frequency = omega and set k= 2 pi / wavelength. set v= f*wavelength 524hzlambda= 345 m/s ; wavelength= 65.8cm thus k = .095. Then for 2pi*f I got an omega of 3292.4. Since we are given amplitude of .02cm .02 sin(.095x -3292.4t) however it asks for D=-.02 for t and x of 0 so we know that the trig function has to equal -1. Thus either .02sin (.095x-3292.4t+3pi/2) or .02cos(.095x-3292.4t+pi). However, according to the homework website, I'm wrong and I don't entirely understand why. If anyone could help out I'd greatly appreciate it.

Explanation / Answer

You r master formula for waves: y = A* sin (kx - omega t + delta) speed = frequency * wavelength = omega / k so k = omega / speed = 2 pi f / speed They don't tell you anything about the phase shift delta, so just forget about it--let it be zero. y = A* sin ((2 pi f / speed)x - 2 pi f t) = A sin (2 pi f (x/speed - t) ) Plug in the numbers, and there you go.

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