Which of the following

Question:

Which of the following equations represents a travelling wave ?

  1. $y=\operatorname{Asin}(15 x-2 t)$

  2. $\mathrm{y}=\mathrm{Ae}^{-x^{2}}(v t+\theta)$

  3. $\mathrm{y}=\operatorname{Ae}^{x} \cos (\omega t-\theta)$

  4. $y=A \sin x \cos \omega t$

Correct Option: 1

Solution:

$\mathrm{y}=\mathrm{F}(\mathrm{x}, \mathrm{t})$

For travelling wave $y$ should be linear function of $\mathrm{x}$ and $\mathrm{t}$ and they must exist as $(\mathrm{x} \pm \mathrm{vt})$ $\mathrm{y}=A \sin (15 x-2 t) \rightarrow$ linear function in $\mathrm{x}$ and $\mathrm{t}$

Option (1) is correct.

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