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Byju's Answer

Standard XII

Physics

Sinusoidal Wave

Which of the ...

Question

Which of the following function correctly represent the travelling wave equation for finite values of $x$ and $t$ ?

y = x^{2} - t^{2}

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y = l o g (x^{2} - t^{2}) - l o g (x - t)

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y = e^{2 x} sin t

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y = cos x^{2} sin t

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Solution

The correct option is B $y = l o g (x^{2} - t^{2}) - l o g (x - t)$
As we know that, the equation of travelling wave is given by
$y = f (x - v t)$ $+ v e x$ direction
$y = f (x + v t)$ $- v e x$ direction
$(a) y = x^{2} - t^{2}$
$= (x - t) (x + t)$
$y = (y_{1}) (y_{2})$
It is the multiplication of two travelling wave which is not a condition of a travelling wave.
$(b) y = cos x^{2} sin t$
$\to$ It is the equation of standing wave. So, it is not a travelling wave
$(c) y =$ log $(x^{2} - t^{2}) -$ log $(x - t)$
$=$ log $\frac{(x^{2} - t^{2})}{(x - t)}$
$y =$ log $(x + t)$
Which represents the equation of travelling wave.
$(d) y = e^{2 x} sin t$
This equation is not in the form of $f (x \pm v t) .$ So, this is not a travelling wave.

Final answer: $(c)$

Suggest Corrections

Similar questions

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