The distance between the crest and trough of a transverse wave is $15 \, cm$. What is the velocity of the wave if its frequency is $1000 \, Hz$?

$300 \, m \, s^{-1}$ In a transverse wave, the distance between a crest and the consecutive trough is equal to half of the wavelength $(\lambda/2)$.
Given, $\lambda/2 = 15 \, cm$.
Therefore, the wavelength $\lambda = 2 \times 15 = 30 \, cm = 0.3 \, m$.
The frequency $f = 1000 \, Hz$.
The velocity of the wave $V$ is given by the formula $V = f \times \lambda$.
Substituting the values, $V = 1000 \times 0.3 = 300 \, m \, s^{-1}$.