The period of a 10 kHz radio wave traveling at 10$^{8}$ ms$^{-1}$ is--

Analyze the question: We are asked for the period of a radio wave with frequency 10 kHz. The wave speed (10⁸ m/s) is extra information, because the period depends only on frequency.

Concept: Period and frequency are reciprocals:

T = 1/f

Solution:

• f = 10 kHz = 10 × 10³ Hz = 10⁴ Hz
• T = 1/f = 1/10⁴ = 1.0 × 10⁻⁴ s

Check the options:

• A (3.0 × 10⁻⁵ s) is wrong. It would come from using 3 × 10⁸ m/s in a wrong calculation, and it does not match 1/f.
• B (1.0 × 10⁻⁴ s) matches our result.
• C and D are far too large. A period of 10⁴ s would mean a very slow wave, not 10 kHz.

Tip: Period questions often include distractors such as speed or wavelength. If you are given frequency and asked for period, just use T = 1/f. Also convert prefixes carefully: k = 10³, M = 10⁶. Speed matters only when you need wavelength (λ = v/f).