Question

The equation of standing wave is y = a cos kx sin `omega"t"`. Which one of following graphs is for the wave at t = T/4?

Options

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Answer 1

Explanation:

For t = `"T"/4`, equation of standing wave is 

`"y"= "a" cos "kx" sin ((2 pi)/"T")("T"/4)`

`= "a" cos "kx" sin π/2`

`="a" cos "kx"="a"cos  (2pi)/lambda "x"`

Now, for x = 0, y = a cos 0=+a

For `"x"= lambda/2, "y" = a cos pi= "-a"`

Only above the graph describes these values.