Question

The wavelength of a radio wave is $1.0m.$ Find its frequency.

Answer 1

hint: To solve this question we have to find the relation between velocity of babe and wavelength of the wave as we know the wavelength is the distance between two consecutive crest or trough for a transverse wave

Complete step by step solution:
We know that the wavelength of the babe is defined as the distance between two consecutive crests or trough is known as wavelength of a transverse wave
Let us assume a transverse wave whose velocity is $v$ in positive X- direction and its wavelength is $\lambda$ and frequency $f$ and it complete one oscillation in time T as soon figure

To complete one oscillation it takes time $T$ called time period
The distance travelled in one time period is defined as Lambda $\lambda$ as you can see in figure
Now we can calculate the velocity of wave
$\Rightarrow v = \dfrac{d}{t}$
Here distance $d = \lambda$ and time $t = T$
$\Rightarrow v = \dfrac{\lambda }{T}$
Here $\dfrac{1}{T}$ is known as oscillation per second so we can say it is the frequency of giving wave
$\because \dfrac{1}{T} = f$
From this we can write
$\Rightarrow v = f\lambda$
$\therefore f = \dfrac{v}{\lambda }$
This is the relation between velocity, frequency and the wavelength of the wave
Now put the given value from question
Velocity of electromagnetic wave is $v = 3.0 \times {10^8}m/s$
$\lambda = 1m$
$\Rightarrow f = \dfrac{{3.0 \times {{10}^8}}}{1}$
$\therefore f = 3.0 \times {10^8}Hz$

Hence the frequency of given wave is $3.0 \times {10^8}Hz.$

Note: There are two types of wave one is transverse and another is longitudinal wave the wavelength for transverse wave defined in the above solution similarly we can define the wavelength of longitudinal wave. The wavelength of longitudinal waves can be defined as the distance between two consecutive compressions or rarefactions is known as the wavelength of longitudinal waves.