Question

A radio station has a frequency of 103.7 MHz. (1 MHz = 10^6 S-1) What is

the wavelength of the radiation emitted by the station?

can someone help asap

Answer 1

Approximately
`2.890\; \rm m` (assuming that the speed of light in air is approximately
`2.997 * 10^(8)\;\rm m \cdot s^(-1)`.)

Step-by-step explanation:

The wavelength of a wave is the distance (the energy of) that wave covers in one cycle of that wave.

On the other hand, the frequency of a wave gives the number of cycles of that wave in unit time. (If the unit of frequency is
`\rm Hz` or
`\rm s^(-1)`, one unit time would be one second.)

First step: calculate the period of this wave. That's the same as finding the duration of each cycle of this wave.

The question states that the frequency of this wave is
`f = 103.7 \; \rm MHz = 103.7 * 10^(6)\; \rm s^(-1)`. In other words, there are
`103.7 * 10^(6)` cycle of this wave in every second.

Each of these cycle have the same length. Therefore, the duration of one such cycle would be:

`\begin{aligned} T &= (1)/(f) \\ &= (1)/(103.7 * 10^(6)\; \rm s^(-1)) \approx 9.64320 * 10^(-9)\; \rm s\end{aligned}`.

That would also be the period of this wave.

Second step: using the speed of this wave, calculate the distance that this wave would travel in each period. That distance would be the wavelength of this wave.

Electromagnetic waves travel at the speed of light. In the air, that speed would be approximately
`2.997 * 10^(8)\;\rm m \cdot s^(-1)`. That is:
`v\approx 2.997 * 10^(8)\;\rm m \cdot s^(-1)`.

The first step shows that the period of this wave is approximately
`9.64320 * 10^(-9)\; \rm s`. Calculate how far this wave would have covered in that much time when travelling at the speed of light in the air:

`\begin{aligned} \lambda &= v \cdot T \\ &\approx 2.997 * 10^(8)\;\rm m \cdot s^(-1) \\ &\quad * 9.64320 * 10^(-9)\; \rm s \\ &\approx 2.890\; \rm m \end{aligned}`.

In other words, the wavelength of this wave in the air would be approximately
`2.890\; \rm m`.