Two waves are described by the wave functions y1 (x, t) = 5 sin(2x – 10t) m, y2
ID: 1670704 • Letter: T
Question
Two waves are described by the wave functionsy1 (x, t) = 5 sin(2x – 10t) m,
y2 (x, t) = 10 cos(2x – 10t)m,
where x is in meters and t in seconds.
1. Show that the wave resulting from their superposition isalso sinusoidal by writing the resulting wave function.
2. What is the amplitude and phase of the resulting wave?
Explanation / Answer
y = y1+y2 = 5*(sin(2x-10t) + 2cos(2x-10t)) Let be the angle such that: tan= 2 => y = 5/cos*(cos*sin(2x-10t) +sin*cos(2x-10t)) = 5/cos *sin(2x-10t +) => y form the formula : y = A.sin(2x-10t +) b) the amplitude : A = 5/cos tan = 2 => cos = 1/5 => A = 55 the phase : 2x-10t + = 2x-10t + arctan(2) = 2x-10t +1.107
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