$A$ source is producing $1500$ sound waves in $3$ seconds. If the distance covered by a compression and an adjacent rarefaction is $68 \, cm$,find $(a)$ frequency,$(b)$ wavelength,and $(c)$ velocity of the sound wave.

(N/A) Number of waves produced in $3 \, s = 1500$.
Number of waves produced in $1 \, s = 1500 / 3 = 500$.
Therefore,frequency,$\nu = 500 \, Hz$.
$(b)$ Wavelength is defined as the distance between two consecutive compressions or two consecutive rarefactions. The distance between a compression and an adjacent rarefaction is half the wavelength $(\lambda / 2)$.
Given,$\lambda / 2 = 68 \, cm$.
Therefore,wavelength,$\lambda = 68 \times 2 = 136 \, cm = 1.36 \, m$.
$(c)$ Velocity,$V = \nu \times \lambda$.
$V = 500 \, Hz \times 1.36 \, m = 680 \, m/s$.