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.

Analyze the question: We need the wavelength (λ) of a radio wave given its frequency and speed.

Concept: The wave equation is

v = fλ, so λ = v / f

Check the data: The question says the speed is 3.0 × 10⁻⁸ m/s. That is almost certainly a typo. The speed of radio waves (electromagnetic waves) is 3.0 × 10⁸ m/s, and a negative exponent would make the wave absurdly slow.

Solution with the question as printed (v = 3.0 × 10⁻⁸ m/s):

• f = 400 kHz = 4.0 × 10⁵ Hz
• λ = (3.0 × 10⁻⁸) / (4.0 × 10⁵) = 0.75 × 10⁻¹³ = 7.5 × 10⁻¹⁴ m

Solution with the physically correct speed (v = 3.0 × 10⁸ m/s):

• λ = (3.0 × 10⁸) / (4.0 × 10⁵) = 0.75 × 10³ = 7.5 × 10² m = 750 m

This value is not among the options. Option E, 7.5 × 10⁻¹⁴ m, has the same digits (7.5) and appears to come from the same typo in the exponent of the speed.

Conclusion: Using the question exactly as written, the calculation gives 7.5 × 10⁻¹⁴ m, so the answer is E. In real life, though, the wavelength of a 400 kHz radio wave is about 750 m, so the question itself contains an error in the speed's exponent. In the exam, go with E, since it is the only option consistent with the given data.

Tip: Always convert units first (kHz → Hz, so multiply by 10³). Then apply λ = v/f. If an answer looks physically unreasonable, recheck the data. Radio waves travel at 3 × 10⁸ m/s.