The wave function of a standing wave on a string fixed at both ends is given by

Question

The wave function of a standing wave on a string fixed at both ends is given by y(x,t)=0.02sin(0.3x)cos(25t), where y and x are in cm and t is in seconds. A) What is the amplitude of the wave? B) What is the wavelength of the standing wave? C) What is the speed of the wave?

Explanation / Answer

in this sinusoidal description of waves: a) the amplitude is the coefficient of the trig function, so amplitude = 3.4mm b) the coefficient, k, is the wave number, and equals 2pi/wavelength, so the wavelength is 1.9=2pi/lambda => lambda=3.31m c) the angular frequency, w, is 2pi/Period, so Period = 2pi/590 =0.01s d) wave speed = wavelength x frequency, so here, speed = 3.31m x 100/s = 331m/s (sounds like a sound wave...ouch, didn't mean that to be a pun) Happy Thanksgiving! (how do you make the Greek symbols the way you do?)

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