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A longitudinal progressive wave is given by the equation y = 5 xx 10^(2) sin pi (400 1 + 1)m. Find (i) amplitude (ii) frequency (iii) wave length and (iv) velocity of the wave (W) velocity and acceleration of particle at x=(1)/(6)m-at=0.1 a(vi) maximum particle velocity and accelerdion. |
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Answer» Solution :Comparing with the general equation of the progressive wave `y=A sin (OMEGA+ kx)` we FIND `omega=400 piand k= pi `, we find (i) `A=5xx10^(-2)m` (ii) `f=(omega)/(2pi)=(400pi)/(2pi)=200 Hz` (iii) `lambda=(2pi)/(k)=(2pi)/(pi)=2m` `(iv) v=(omega)/(k)=(400pi)/(pi)=400 ms^(-1)` (v) `v_(p)= A omega cos (omega t+kx)=10 sqrt(3) pi ms^(-1)` `a_(p)=A omega^(2) sin (omegat+kx)=-4xx10^(-4) ms^(-2)` `(vi) V_(max)=A omega =20 pi ms^(-1)` |
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