Question

If the frequency of a radio station is 88.1 MHz (8.81 x 107 Hz), what is the wavelength of the wave used by this radio

station for its broadcast? The answer should have three significant figures.
meters

Answer 1

3.41

Step-by-step explanation:

Breed=different

Answer 2

Approximately
`3.40\; \rm m`.

Step-by-step explanation:

In the earth's atmosphere, the speed of radio waves is very close to that of light in vacuum.

• 
  `v \approx 2.99792* 10^8\; \rm m \cdot s^(-1)`.
• In other words, the radio wave from the station would travel
  `2.99792* 10^8` meters in each second.
• Note that the answer should have three significant figures. To avoid rounding errors, make sure all intermediate values have more significant figures than that. Here,
  `v` has six significant figures.

The frequency
`f` of a wave gives the number of cycles in unit time. That's the same as the number of wavelengths that this wave covers in unit time.

In this question,
`f = 8.81 * 10^7\; \rm Hz = 8.81 * 10^7\; \rm s^(-1)`. In other words, in each second, this wave would travel a distance that's equal to
`8.81 * 10^7` times its wavelength.

Let
`\lambda` represent the wavelength of this wave.

`\begin{aligned}& 8.81 * 10^(7)\, \lambda \\ &= \text{Distance this wave travels in $1$ s}\\ &\approx \text{Distance light travels in vacuum in $1$ s} \\ &\approx 2.99792 * 10^(8)\; \rm m\end{aligned}`.

Hence the equation:

`8.81 * 10^(7)\, \lambda \approx \rm 2.99792 * 10^(8)\; m`.

`\begin{aligned}\lambda &= (2.99792 * 10^(8))/(8.81 * 10^(7)) \rm \; m\approx 3.40\; m\end{aligned}`.

(Rounded to three significant figures.)

In general, if a wave has speed
`v` and frequency
`f`, then its wavelength would be:

`\displaystyle \lambda = (v)/(f)`.