Wavelength to Frequency Formula

Wavelength to Frequency Formulas - Definitions & Practice Questions

The wavelength of a wave is inversely related to its frequency. If v represents the velocity of a wave, \[\nu \], its frequency and \[\lambda \]its wavelength, then;
\[v = \nu \,\lambda \]
Or \[\lambda = \frac{v}{\nu }\]
This means, as wavelength increases, frequency will decrease and vice versa.
In the case of light in vacuum, this formula is given as: \[\lambda = \frac{c}{\nu }\]
Example:
A typical sound wave travelling at 360 m/s has a frequency of 1200 Hz. Find its wavelength.
Solution:
\[\nu \] = 1200 Hz, v = 360 m/s, \[\lambda \]=?
\[\lambda = \frac{v}{\nu } = \frac{{360}}{{1200}} = 0.3\,m\]

Question:
All electromagnetic waves travel through vacuum at the same speed. If a wave of frequency 7.5 GHz has a wavelength 4 cm, then the frequency of a wave with wavelength 6 km will be (assume both are electromagnetic waves propagating in vacuum):
Options:
(a) 40 kHz
(b) 50 kHz
(c) 5 GHz
(d) 2.5 MHz
Answer: (b)