A sound of frequency 512 Hz reaches a listener 100 m away. If the sound travels in air at s.t.p., what is its wavelength? [speed of sound in air = 331 m/s]

Analyze the question: We're given the frequency of a sound (512 Hz) and the speed of sound in air (331 m/s). We need the wavelength. The 100 m distance is extra information and doesn't affect the wavelength.

Concept: For any wave, the speed, frequency and wavelength are related by:

v = fλ, so λ = v / f

Solution:

λ = 331 / 512

λ ≈ 0.6465 m

Rounded to three significant figures, λ ≈ 0.646 m (the "0,646" in option B uses a comma as the decimal point).

Checking the other options:

• A (1.550 m): this would need a frequency of about 213 Hz.
• C (5.120 m): this comes from mixing up the numbers, and is far too large.
• D (0.195 m): this would need a frequency of about 1700 Hz.

Answer: B. 0.646 m

Exam tip: In WASSCE and JAMB, extra data such as the 100 m distance is often included to distract you. Always ask which quantities the formula actually needs. Also, a quick estimate helps: 331 ÷ 512 is a bit more than 330 ÷ 500 = 0.66, so the answer should be a little below 1 m. That immediately rules out A and C.