A radio station broadcasts at a frequency of 400 kHz. If the speed of the wave is 3.0 ×10\(^{-8}\)ms\(^{-1}\), calculate the wavelength of the radio wave.
To calculate the wavelength of a radio wave, we use the formula:
\(\lambda = \frac{v}{f}\)
where:
- \( v \) is the speed of the wave,
- \( f \) is the frequency.
Given:
- Frequency \( f = 400 \, \text{kHz} = 400 \times 10^3 \, \text{Hz} \)
- Speed \( v = 3.0 \times 10^{-8} \, \text{m/s} \)
Substituting the values into the formula:
\(\lambda = \frac{3.0 \times 10^{-8} \, \text{m/s}}{400 \times 10^3 \, \text{Hz}}\)
Calculating:
\(\lambda = \frac{3.0 \times 10^{-8}}{4.0 \times 10^5}\)
\(\lambda = 7.5 \times 10^{-14} \, \text{m}\)
Thus, the wavelength of the radio wave is:
\(\lambda = 7.5 \times 10^{-14} \, \text{m}\)
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