Question

Wavelength ($\lambda$), frequency $\left(f\right)$ and velocity $\left(v\right)$ of a sound wave are related as:

• A. $\lambda =v\times \frac{1}{f}$
• B. $\frac{\lambda }{f}=v$
• C. $\lambda \times v=f$
• D. $f\times v=\frac{1}{\lambda }$

Answer 1

The correct option is A $\lambda =v\times \frac{1}{f}$

The wave travels one wavelength $\left(\lambda \right)$ of distance in one time period $\left(T\right)$.
So, using the formula for speed is:
$v=\frac{\lambda }{T}$

But, time period is inverse of frequency.
$f=\frac{1}{T}$

$⟹v=f\times \lambda$
From this relationship, we get:
$\lambda =v\times \frac{1}{f}$