A progressive wave travelling in a medium is represented by the...

The given equation of the progressive wave is $y = A \sin(\beta t - \alpha x)$.

Comparing this with the standard equation of a progressive wave $y = A \sin(\omega t - k x)$, we get the angular frequency $\omega = \beta$ and the wave number $k = \alpha$.

The wave number $k$ is related to the wavelength $\lambda$ by the relation $k = \dfrac{2\pi}{\lambda}$.

Substituting $k = \alpha$, we get $\alpha = \dfrac{2\pi}{\lambda}$.

Therefore, the wavelength is $\lambda = \dfrac{2\pi}{\alpha}$.

Answer: $\dfrac{2\pi}{\alpha}$