Respuesta :
Answer:
Approximately [tex]3.40\; \rm m[/tex].
Explanation:
In the earth's atmosphere, the speed of radio waves is very close to that of light in vacuum.
- [tex]v \approx 2.99792\times 10^8\; \rm m \cdot s^{-1}[/tex].
- In other words, the radio wave from the station would travel [tex]2.99792\times 10^8[/tex] 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, [tex]v[/tex] has six significant figures.
The frequency [tex]f[/tex] 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, [tex]f = 8.81 \times 10^7\; \rm Hz = 8.81 \times 10^7\; \rm s^{-1}[/tex]. In other words, in each second, this wave would travel a distance that's equal to [tex]8.81 \times 10^7[/tex] times its wavelength.
Let [tex]\lambda[/tex] represent the wavelength of this wave.
[tex]\begin{aligned}& 8.81 \times 10^{7}\, \lambda \\ &= \text{Distance this wave travels in $1$ s}\\ &\approx \text{Distance light travels in vacuum in $1$ s} \\ &\approx 2.99792 \times 10^{8}\; \rm m\end{aligned}[/tex].
Hence the equation:
[tex]8.81 \times 10^{7}\, \lambda \approx \rm 2.99792 \times 10^{8}\; m[/tex].
[tex]\begin{aligned}\lambda &= \frac{2.99792 \times 10^{8}}{8.81 \times 10^{7}} \rm \; m\approx 3.40\; m\end{aligned}[/tex].
(Rounded to three significant figures.)
In general, if a wave has speed [tex]v[/tex] and frequency [tex]f[/tex], then its wavelength would be:
[tex]\displaystyle \lambda = \frac{v}{f}[/tex].
