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Check whether, the following equations c...

Check whether, the following equations can represent a progressive (travelling wave)
(a) `y=A cos(x^(3)-vt) (b) x=Ae^((vt-y))(c) y=A log((x)/(v)-t)`

Text Solution

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(a) Since the factor `(x^(3)-vt)`, cannot be expressed in terms of the combination of `(x+-vt)` and /or some constants, so, the equation cannot represent a wave.
(b) For a finite value of .y. after a long time,`t to oo` the factore `e^(vt-y)oo,`as such the displacement x is undefined for `vt-y lt` ,so, the equation doesnot represent a wave.
(c) Since the value of log `((x)/(v)-t)` is undefined for `(x)/(v)-t le 0`, so the equation cannot pertain toa wave
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