Wavelength and frequency in a progressive wave

Steps:

• In the diagram of the sound wave, points P and Q are separated by a distance L, corresponding to half a wavelength (from crest to trough or antinode to node).
• Thus, the full wavelength λ equals 2L.
• The wave speed v relates to frequency f and wavelength by v = fλ.
• Substitute λ = 2L to get f = v / (2L).

Why A is correct:

• A gives f = v/(2L), which follows directly from the wavelength formula when L is half the wavelength in a longitudinal sound wave.

Why the others are wrong:

• B assumes L is the full wavelength, overestimating frequency.
• C assumes L is quarter wavelength, doubling the actual frequency.
• D gives the period T = L/v, not frequency.

Final answer: A