Question

The relation between frequency $\left(n\right)$ and wavelength $\left(\lambda \right)$ of a sound wave is given by

($v$ is velocity, $n$ is frequency and $T$ is time-period)

• A. $v=n\lambda$
• B. $n=-v\lambda$
• C. $v=\frac{n}{2\lambda }$
• D. $n=\frac{T}{\lambda }$

Answer 1

The correct option is A $v=n\lambda$

Time period $\left(T\right)$ of a wave is defined as the time taken to produce one complete wave, and frequency $\left(n\right)$ of a wave is defined as the number of complete waves produced in unit time.

Thus they are related as,

$n=\frac{1}{T}$ or $T=\frac{1}{n}$

In one time period (T), a wave advances by a distance equal to one

wavelength. Thus if $v$ is the velocity of the given wave, it is given by,

$v=\frac{\lambda }{T}$

As $n=\frac{1}{T}$, we may write,

$v=n\lambda$