A sinusoidal wave is described by the wave function, y = ( 0.24 m) sin( 0.20 x 5

Question

A sinusoidal wave is described by the wave function, y = (0.24 m) sin(0.20x 50t) where x and y are in meters and t is in seconds. Determine the following for this wave. (a) the amplitude
1 m

(b) the angular frequency
2 rad/s

(c) the angular wave number
3 rad/m

(d) the wavelength
4 m

(e) the wave speed
5 m/s

(f) the direction of motion 6 +x x     +y y A sinusoidal wave is described by the wave function, y = (0.24 m) sin(0.20x 50t) where x and y are in meters and t is in seconds. Determine the following for this wave. (a) the amplitude
1 m

(b) the angular frequency
2 rad/s

(c) the angular wave number
3 rad/m

(d) the wavelength
4 m

(e) the wave speed
5 m/s

(f) the direction of motion 6 +x x     +y y A sinusoidal wave is described by the wave function, y = (0.24 m) sin(0.20x 50t) where x and y are in meters and t is in seconds. Determine the following for this wave. (a) the amplitude
1 m

(b) the angular frequency
2 rad/s

(c) the angular wave number
3 rad/m

(d) the wavelength
4 m

(e) the wave speed
5 m/s

(f) the direction of motion 6 +x x     +y y y = (0.24 m) sin(0.20x 50t) (a) the amplitude
1 m

(b) the angular frequency
2 rad/s

(c) the angular wave number
3 rad/m

(d) the wavelength
4 m

(e) the wave speed
5 m/s

(f) the direction of motion 6 +x x     +y y 6 +x x     +y y 6 +x x     +y y 6

Explanation / Answer

The given wavefunction is y = (0.24 m) sin(0.20x 50t) we have an equation for the wave as y = A sin(kx - t) By comparing the above two equations we get, a) Amplitude, A = 0.24 m b) Angular frequency = /2 = 50/(2*3.14) = 7.96 Hz c) The wave number, k = 0.2 rad/m d)We have an equation for the wave number, k = 2/ from this the equation for the wavelength, = 2/k = 2*3.14 / 0.2 = 31.4 m e) The wave speed is given by, v = /k = 50/0.2 = 250 m/s f) The direction of the wave is to the right. i.e. towards positive x- axis. f)

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