What is the amplitude and frequency of the resultant wave? (Please Help)?

Two traveling sinusoidal waves are described by the wave functions where x, y1 and y2 are in meters and t is seconds.

y1 = (5.45 m) sin[(4.30x - 1260t)]


y2 = (5.45 m) sin[(4.30x - 1260t - 0.25)]

a) What is the amplitude of the resultant wave?

b) What is the frequency of the resultant wave?

Thank You

2 Answers

  • You can use the trig identity sin u + sin v = 2 sin(½(u+v)) cos(½(u−v)) with u=4.30x - 1260t and v=4.30x - 1260t - 0.25. You should find that the resultant wave is given by 2*(5.45m)* sin(4.3x-1260t-.125) *cos(.125). That means:

    a) The amplitude is 2*(5.45m)*cos(.125) =10.81m

    b)The frequency is the same as it was for y1 and y2: the angular frequency w =1260 rad/s or f = w/(2*Pi) = (1260 rad/s)/(2*Pi rad) = 200.5 Hz.

    Hope that helps!

  • a) = 2(5.45)cos(0.125) = 10.815

    b) = (1260 x Pi) / (2 x Pi) => = 1260/2 = 630

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