The equation of a stationary wave is given by , 100cossin2),( t xtxy where x and y are measured in metre and t in second. Calculate the amplitude, wavelength and frequency of component waves whose superposition generated this stationary wave. Also write the equations of component waves.
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Given stationary wave : y(x,t)= 100 cos x * sin 2t
y(x,t) = 50 [sin (2t + x) + sin (2t - x) ]
component waves: y1(x,t) = 50 sin (2t +x)
and y2(x,t) = 50 sin (2t -x)
Amplitude, frequency and wave number are same for both waves. The direction of y2(x,t) is in +ve x direction and y1(x,t) is towards -ve x axis.
Amplitude = 50 frequency = 2 rad/sec = 1/pi Hz
wave number = k = 1 /meter
y(x,t) = 50 [sin (2t + x) + sin (2t - x) ]
component waves: y1(x,t) = 50 sin (2t +x)
and y2(x,t) = 50 sin (2t -x)
Amplitude, frequency and wave number are same for both waves. The direction of y2(x,t) is in +ve x direction and y1(x,t) is towards -ve x axis.
Amplitude = 50 frequency = 2 rad/sec = 1/pi Hz
wave number = k = 1 /meter
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