Question

A radio station broadcasts at $760\,Hz$. What is the wavelength of the station?
A. $395\,m$
B. $790\,m$
C. $760\,m$
D. $197.5\,m$

Answer 1

In order to solve this question we need to understand how radio stations send frequencies and how do we listen to them on our radio? Radio station transmits wave at particular frequency my modulating the wave so that there would be less noise involved with wave then in our radio we tune the frequency by turning knob so that we get exact frequency matches then, resonance happens after which devices used in radio converts the wave energy into sound energy so that we can listen.

Complete step by step answer:
Given the frequency of the radio wave, $f = 760\,Hz$. Since the speed of all electromagnetic waves in free air is the speed of light which is $v = 3 \times {10^8}m\,{\sec ^{ - 1}}$. Let the wavelength of the radio wave be $\lambda$.
So, by using relation,
$f\lambda = v$
So wavelength is,
$\lambda = \dfrac{v}{f}$
Putting values we get,
$\lambda = \dfrac{{3 \times {{10}^8}m\,{{\sec }^{ - 1}}}}{{760 \times {{10}^3}{{\sec }^{ - 1}}}}$
$\therefore \lambda = 394.736\,m$

So the correct option is A.

Note: It should be remembered that here the light travels in air so according to postulates of special theory of relativity light speed is always constant in all inertial frames but when a light travels in medium its speed changes due change in refractive index of the medium. Frequency of light is defined as the number of oscillations that a wave makes in one second and wavelength is defined as distance between consecutive crest and trough of wave. Crest is defined as the point at which waves have maximum displacement and trough is defined as the point at which waves have minimum distance.