Physics Question of the Day

1. It becomes $1/2$ as large
2. It becomes $1/4$ as large (correct answer)
3. It becomes 2 times as large
4. It becomes 4 times as large

Explanation: This question tests understanding of the relationship between wave amplitude and wave energy. Wave energy is proportional to the amplitude squared: E ∝ A², which means if you double the amplitude (A → 2A), the energy increases by a factor of 4 (E → 4E), and if you halve the amplitude (A → A/2), the energy decreases by a factor of 4 (E → E/4)—this squared relationship is fundamental to all types of waves including sound, water, seismic, and light waves. When amplitude is reduced to half its original value (A → A/2), we calculate the intensity change using the squared relationship: I₂/I₁ = (A₂/A₁)² = (A/2 / A)² = (1/2)² = 1/4, so the intensity becomes 1/4 as large—halving the amplitude reduces intensity to one-quarter of its original value. Choice B is correct because it properly applies the squared relationship I ∝ A² to show that halving amplitude reduces intensity to 1/4. Choice A incorrectly treats the relationship as linear (I ∝ A), claiming that halving amplitude halves intensity, when actually the relationship is quadratic (I ∝ A²) so halving amplitude reduces intensity to one-quarter—this is why the answer is 1/4, not 1/2. To solve amplitude-energy problems, remember the formula E₂/E₁ = (A₂/A₁)²: (1) if asked how energy changes when amplitude changes, square the amplitude factor (if A is halved, E becomes (1/2)² = 1/4), (2) if asked how amplitude changes when energy changes, take the square root of the energy factor (if E becomes 1/4, A becomes √(1/4) = 1/2), and (3) always check your answer makes sense—smaller amplitude must mean less energy, and the relationship is stronger than linear (energy decreases faster than amplitude). Physical intuition: the squared relationship makes sense because wave energy depends on both how far the electric field oscillates (amplitude) and how much energy is stored in the field—both effects scale with amplitude, so total intensity scales as amplitude squared; this is why dimming a light by reducing the electric field amplitude to half produces a light that appears much dimmer than half brightness, as it actually has only 1/4 the intensity.