The displacement of a particle in standing wave on a string is given by y ( x , t ) = 0.4 sin ⁡ ( 0.5 x ) cos ⁡ ( 30 t ), where x and y are in cm. Identify the incorrect option - AFrequency of wave is 15π Hz BWave speed is 130 cm/s CAmplitude of wave is 0.2 cm DWave number for the wave is 0.5 cm^−1

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The displacement of a particle in standing wave on a string is given by   y  (  x  ,  t  )  =  0.4  sin  ⁡  (  0.5  x  )  cos  ⁡  (  30  t  ), where x and y are in cm. Identify the incorrect option - AFrequency of wave is 15π Hz BWave speed is 130 cm/s CAmplitude of wave is 0.2 cm DWave number for the wave is 0.5 cm^−1

Kathryn Boyer · Accepted Answer

Wave speed is 130 cm/sGiven:y(x,t)=0.4sin(0.5x)cos(30t) On comparing with standard equation of standing waves,y(x,t)=2Asin(kx)cos(ωt) We get, Amplitude, A=0.2 cm Wave number, k=0.5 cm−1 Angular frequency, ω=30 rad/s So, frequency, f=ω2π=302π=15π Hz Wave speed, v=ωk=300.5=60 cm/s

The displacement of a particle in standing wave on a string is given by y(x,t)=0.4sin(0.5x)cos(30t), where x and y are in cm.

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