Two traveling sinusoidal waves are described by the wave functions y1 = 5.46 sin
ID: 1656103 • Letter: T
Question
Two traveling sinusoidal waves are described by the wave functions y1 = 5.46 sin [(4.42x 1243t)] y2 = 5.46 sin [(4.42x 1243t 0.250)] where x, y1, and y2 are in meters and t is in seconds.The sum of two wave functions y1 and y2 traveling in the same direction having the same amplitude Ao angular frequency and wave number k but differing in phase, have the resultant wave function y=y1 + y2 = 2A0 cos )sin ( kx-at- where is the phase constant that determines the phase difference between y and y2 based on their initial conditions. (a) The amplitude of this resultant wave is A -2Ao cos m) cos m, (b) and its frequency is 2T Hz.
Explanation / Answer
Given,
y1 = 5.46 sin [(4.42x 1243t)]
y2 = 5.46 sin [(4.42x 1243t 0.250)]
a)y = y1 + y2
y = 5.46 {sin [(4.42x 1243t)] + sin [(4.42x 1243t 0.250)}
theta = 4.42x - 1243t ; implies y2 is leading y1 by pi/4
A = 2 A cos(phi/2)
A = 2 x 5.46 x cos(pi/8) = 10.09 ,
Hence, A = 10.09 m = 10.1 m
b)f = w/2pi
w = 1243
f = 1243 pi/2 pi = 621.5 Hz
Hence, f = 621.5 Hz
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.