A radio station broadcast at a frequency of 600KHZ. If the speed of light in air is 3 × 108ms$^{−1}$. Calculate the wavelength of the radio wave

Analysis

To solve this problem, we need to relate the speed of a wave, its frequency, and its wavelength. This is a classic wave equation problem frequently tested in JAMB Physics.

Concept

The relationship between the speed of a wave ($v$), its frequency ($f$), and its wavelength ($\lambda$) is given by the formula:

Where:

• $v$ = speed of light ($3 \times 10^8 \text{ m/s}$)
• $f$ = frequency (in Hertz)
• $\lambda$ = wavelength (in meters)

To find the wavelength, we rearrange the formula:

Step-by-Step Solution

Step 1: Convert units to SI units. The frequency is given in kilohertz (kHz). We must convert this to Hertz (Hz):

• $f = 600 \text{ kHz} = 600 \times 10^3 \text{ Hz}$
• $f = 6 \times 10^5 \text{ Hz}$

Step 2: Apply the formula. Substitute the values into the rearranged equation:

Step 3: Perform the calculation.

• Divide the coefficients: $3 \div 6 = 0.5$
• Divide the powers of 10: $10^8 \div 10^5 = 10^{(8-5)} = 10^3$
• Combine them: $\lambda = 0.5 \times 10^3 \text{ m}$

Step 4: Convert to standard scientific notation.

• $0.5 \times 10^3 = 5 \times 10^{-1} \times 10^3 = 5 \times 10^2 \text{ m}$

Conclusion

Comparing our result to the given options, we find that $5.0 \times 10^2 \text{ m}$ matches option B.

Exam Tip

Always watch out for prefixes like k (kilo = $10^3$), M (mega = $10^6$), or n (nano = $10^{-9}$). JAMB examiners love to test your ability to convert these prefixes to standard SI units before plugging them into your formulas. If you forget to convert kHz to Hz, your answer will be off by a factor of 1,000!