Short on time? This page is the recap. For explanations, Figures 1 and 2 and the worked examples, use the full study guide.
Recap
- At a boundary between two media a wave is partly reflected and partly transmitted. The two new waves share the incident energy, so each has a smaller amplitude.
- The reflected pulse is inverted if the wave slows down in the new medium, and upright if it speeds up. The transmitted pulse is always upright.
- Limiting cases: a fixed end reflects everything, inverted; a free end reflects everything, upright.
- Frequency and period do not change at a boundary. Wavelength and pulse width change in proportion to speed.
- A polarized transverse wave oscillates in one direction. Longitudinal waves (such as sound) cannot be polarized.
- Waves can be polarized by a filter (or slot), by reflection from a surface and by refraction.
- Polarizing a wave usually reduces its intensity, the average power per unit area over one period.
Key relationships
| Relationship | Symbols and units | Use it to |
|---|---|---|
| v = √(F_T/μ) | F_T in N, μ in kg/m | compare speeds on two strings |
| λ₂/λ₁ = v₂/v₁ (f fixed) | λ in m, v in m/s | find the new wavelength or pulse width |
| I = P/A | P in W, A in m², I in W/m² | find intensity or power |
| Ideal filter, unpolarized light in | I = I₀/2 | find intensity after one filter |
| Ideal filter, polarized light in | all passes if parallel, none if perpendicular | predict crossed or aligned filters |
Assumptions behind the numbers
- Strings that are tied together have the same tension.
- Filters are ideal unless the question says otherwise.
- Light falls on a surface at right angles when you use I = P/A.
Mistakes to avoid
- Changing the frequency at a boundary. Only v and λ change.
- Inverting the transmitted pulse. Only the reflection can flip.
- Giving the reflected pulse the new speed. It is still in the first medium.
- Saying sound can be polarized. It is longitudinal.
- Halving the intensity at the second filter. The ½ rule is only for unpolarized light; after that, the angle between the axes decides.
- Confusing intensity and power. Intensity is power per square metre.
Quick self-check
- A pulse goes from a heavy rope into a light rope under the same tension. Is the reflected pulse inverted? (No. The wave speeds up, so the reflection is upright.)
- A 10 Hz wave moves at 40 m/s and then enters a medium where it moves at 15 m/s. What are the two wavelengths? (4.0 m, then 1.5 m)
- Unpolarized light of intensity 120 W/m² passes through one ideal polarizing filter. What intensity leaves? (60 W/m²)
Next: practice questions.