Question

What is the wavelength of a radio station of frequency $99$ MHz (megahertz)? The speed of electromagnetic waves is $3 \times {10^8}$ m/s.

Answer 1

Hint: The measure of the length of the complete wave cycle is known as the wave-length. The distance travelled by the wave from the point is known as the velocity. First convert the given unit of the wavelength in the MKS system. Convert nano-metre in metre. And then substitute the values in the standard formula stating relation between the velocity and wavelength and simplify.

Formula used:
$v = \lambda \times f$
Here $v$ is the velocity of light, $\lambda$ is the wavelength and $f$ is the frequency.

Complete step by step answer:
Given that- the frequency of the wavelength is $f = 99\,MHz$
Convert megahertz to hertz
$f = 99 \times {10^6}\,Hz$
Speed of the light is $v = 3.00 \times {10^8}{\text{m/s}}$
Now, according to the formula –
Velocity of the light, $v = \lambda \times f$
Place the known values in the above equation
$3 \times {10^8} = \lambda \times 99 \times {10^6}$
Make the required term the subject -
$\lambda = \dfrac{{3 \times {{10}^8}}}{{99 \times {{10}^6}}}$
The terms with the same power and exponents in the division cancels each other. Simplify as per the required answer
$\therefore \lambda = 3.03\,m$

Hence, the wavelength of a radio station of frequency $99$ MHz is $3.03\,m$.

Note: Remember the difference between the frequency wavelength and the wave velocity. The distance travelled by the wave in the medium during the time a particle completes one vibration is the wavelength. Wave velocity is equal to the product of frequency and the wavelength.