Waves: NEET previous year questions

The spatial part of the phase is $2\pi(0.0080)x$ with x in cm, so the wave number term gives phase difference $\Delta\phi = 2\pi(0.0080)\,\Delta x$. Converting the separation to centimetres, $\Delta x = 0.5\ \text{m} = 50\ \text{cm}$, so $\Delta\phi = 2\pi \times 0.0080 \times 50 = 0.8\pi$ rad (option (2)). The wrong answers arise from failing to convert 0.5 m into 50 cm.

An open-open pipe has antinodes at both ends, and its $p$-th harmonic contains exactly $p$ nodes, so the 5th harmonic gives $n = 5$. A closed pipe supports only odd harmonics, with a node at the closed end and an antinode at the open end; its $q$-th harmonic ($q$ odd) contains $\frac{q+1}{2}$ nodes, so the 9th harmonic gives $m = \frac{10}{2} = 5$. The ratio is therefore 1. NCERT Class 11, Waves (standing waves in air columns).

Initially |fB - 530| = 6. Decreasing B's tension lowers fB; because the beat frequency then increases, B was already below 530 Hz. Thus fB = 530 - 6 = 524 Hz. Chapter: Waves.