Sound waves consist of 20 compressions and 20 rarefactions in 10 meter length.…

For a longitudinal wave such as a sound wave, one complete wave cycle (one wavelength) consists of exactly one compression together with its immediately adjacent rarefaction — a compression and a rarefaction are never counted as two separate cycles. If a length L contains N complete compression-rarefaction cycles, the wavelength is given by wavelength = L ÷ N.

1. The 10 m length contains 20 compressions and 20 rarefactions, i.e. N = 20 complete cycles, since each compression pairs with one adjacent rarefaction.

2. Apply wavelength = L ÷ N = 10 m ÷ 20 = 0.5 m.

3. Convert to centimetres: 0.5 m = 50 cm.

Check: 20 wavelengths of 0.5 m each span 20 × 0.5 m = 10 m, matching the given length — confirming the wavelength is 50 cm.