A wave traveling along the x-axis is described mathematicallyby the equation y = 0.50 sin (16.4t + 0.84x),where y is the displacement (in meters), t is in seconds, and x isin meters. a) What is the wavelength of the wave? b) What is the periodof the wave? c) What is the velocity of the wave? A wave traveling along the x-axis is described mathematicallyby the equation y = 0.50 sin (16.4t + 0.84x),where y is the displacement (in meters), t is in seconds, and x isin meters. a) What is the wavelength of the wave? b) What is the periodof the wave? c) What is the velocity of the wave?
Explanation / Answer
Given y = 0.50 sin (16.4t + 0.84x) compare this with y = A sin ( wt + kx ) then Amplitude A = 0.5 m angular frequency w = 16.4 propagation constant k = 0.84 wavelength = 2 / k = 2.38 m period T = 2 / w = 0.1219 s Velocity v = w / k = 19.52 m / s