Question

The relation between frequency $\upsilon$ , wavelength $\lambda$ and velocity of propagation of wave $v$ is
A. $\upsilon = \dfrac{\lambda }{v}$
B. $\upsilon = \lambda v$
C. $\upsilon = \dfrac{v}{\lambda }$
D. None of these

Answer 1

First let us see what frequency, wavelength and velocity of propagation of wave is-
Frequency is known as the number of waves that reach a fixed point in unit time. It is also known as the cycles or movements encountered by a body in continuous motion within a single unit of time.
The distance from one crest to another or from one trough to another is the wavelength of a wave.
Velocity of the wave is the distance crossed by a periodic or cyclic motion per unit of time.

Complete step by step answer:
Now let us establish the relationship between frequency $\upsilon$ , wavelength $\lambda$
and velocity of propagation of wave $v$-
Since, wave frequency is the number of waves per unit time, and the duration is basically the number of seconds per wave, the frequency- period relationship is-
$\upsilon = \dfrac{1}{T}$

$T = \dfrac{1}{\upsilon }$ ...... (1)
Where $\upsilon$ is the frequency and $T$ is the time period.
The propagation velocity is the distance at a given moment that the wave travels and is one wavelength in a span of one period. In equation it is written as-
$v = \dfrac{\lambda }{T}$

From equation (1), we get-
$v = \upsilon \lambda \\\ \upsilon = \dfrac{v}{\lambda } \\\$

So, the correct answer is “Option C”.

Note:
For a constant frequency, the velocity and wavelength are directly proportional.
The relationship between speed, distance and time is the secret to the simple wave relationship. With this we get the relationship between wavelength, velocity and time period. Also, the velocity of the wave is heavily dependent on the medium in which the wave propagates. But for frequency when a wave travels from one medium to another, it stays the same.