Transverse vs Longitudinal Waves
| Property | Transverse | Longitudinal |
|---|---|---|
| Particle motion | Perpendicular to propagation | Parallel to propagation |
| Examples | String, water surface, light | Sound in air/liquid/solid |
| Can travel in | Solids and on surfaces | Solids, liquids, gases |
| Polarisation | Possible | Not possible |
| Features | Crests and troughs | Compressions and rarefactions |
| Wave equation | y = A sin(kx − ωt) | Same mathematical form |
Open vs Closed Organ Pipe
| Property | Open Pipe | Closed Pipe |
|---|---|---|
| End conditions | Antinodes at both ends | Node (closed), antinode (open) |
| Harmonics present | All (1st, 2nd, 3rd…) | Odd only (1st, 3rd, 5th…) |
| Fundamental f_{1} | v/(2L) | v/(4L) |
| 1st overtone | 2f_{1} (2nd harmonic) | 3f_{1} (3rd harmonic) |
| Richness of tone | Richer (more harmonics) | Simpler (fewer harmonics) |
| Same length comparison | f_{1}open = 2 × f{1}_closed | f_{1}closed = ½ × f{1}_open |
Spring vs Pendulum
| Property | Spring-Mass | Simple Pendulum |
|---|---|---|
| Period formula | T = 2π | T = 2π |
| Depends on | Mass m, spring constant k | Length L, gravity g |
| Independent of | Amplitude, gravity | Mass, amplitude (θ < 15°) |
| Works in zero gravity? | Yes | No (T → ∞) |
| Effect of doubling m | T increases by √2 | No change |