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A stationary wave is described by the equation `y=10sin(x//3)cos(15pit),` where x is in cm and time t is in second. Calculate frequency and velocity of component waves. Also, find the amplitude of stationary waves at antinodes and find the position of first antinode. |
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Answer» The given eqn. is `y=10sin(x//3)cos15pit` Comparing with the standard form of eqn. `y=2sinkxcosomegat, ` we get `2r=10cm, k=(2ppi)/(lambda)=(1)/(3), omega=15pi` `lambda=6pi=6xx3.14=18.84cm` `omega =2piv=15pi,v=7.5Hz` `upsilon=vlambda=7.5xx18.84=141.3cms^(-1)` Amplitude of stationary wave `=10sin((x)/(3))` At antinode, amplitude is maximum, `sin((x)/(3))=max. :. (x)/(3)=pi//2 x=(3pi)/(2)=4.71cm` Amplitude of stationary wave at antinode `=10sin(x//3)=10xx1cm=0.1m` |
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