A wave travelling on a string stretched along the X -axis has an...

The argument of the exponential function must be dimensionless. Therefore, the terms $\dfrac{x}{a} and$\dfrac{t}{T}$are dimensionless.<br><br>Since$x$represents position, its dimension is$L$. For$\dfrac{x}{a}$to be dimensionless, the dimension of$a$must be$L$.<br><br>Since$t$represents time, its dimension is$T$. For$\dfrac{t}{T}$to be dimensionless, the dimension of$T$must be$T$.<br><br>The exponential term$e^{-\left(\dfrac{x}{a} + \dfrac{t}{T}\right)^2} is a dimensionless quantity. Therefore, the dimension of $A$ must be the same as the dimension of $y$.

Since $y$ represents the displacement of the wave, its dimension is $L$. Thus, the dimension of $A$ is $L$.

The dimensions of $A$, $a$, and $T$ are $L$, $L$, and $T$ respectively.