This question tests understanding that wave energy is proportional to amplitude squared (E ∝ A²), meaning larger amplitude waves carry significantly more energy than smaller amplitude waves. The energy-amplitude relationship E ∝ A² creates dramatic effects: doubling amplitude quadruples energy (2× amplitude → 2² = 4× energy), tripling amplitude increases energy nine-fold (3× → 3² = 9×), and increasing amplitude by factor of 10 increases energy by factor of 100 (10× → 10² = 100×)—this squared relationship means small changes in amplitude produce large changes in energy, which explains why loud sounds (large amplitude) are so much more energetic than quiet sounds (small amplitude), why bright lights carry much more energy than dim lights, and why large ocean waves are so powerful compared to ripples (a 2 m wave has 10,000× more energy than a 2 cm ripple: (200 cm / 2 cm)² = 100² = 10,000). For comparing multiple waves: Given three waves with amplitudes 1 cm, 2 cm, and 3 cm, ranking by energy requires calculating E ∝ A² for each: 1 cm: E ∝ 1² = 1 (lowest, reference), 2 cm: E ∝ 2² = 4 (4× more than 1 cm), 3 cm: E ∝ 3² = 9 (9× more, highest)—energy ranking follows amplitude ranking (1 < 2 < 3 cm by amplitude gives 1 < 4 < 9 by energy), but energy differences are larger than amplitude differences (3 cm is 3× taller than 1 cm, but has 9× more energy). Choice B is correct because it properly identifies wave with larger amplitude has more energy and ranks them accordingly using the squared relationship. Choice A compares reversed: claims smaller amplitude has more energy when larger amplitude always has more (E ∝ A² with positive proportionality). The E ∝ A² relationship has important practical implications: (1) safety: doubling volume (amplitude) on speakers quadruples energy delivered to ears (2× amplitude → 4× energy, why prolonged loud music damages hearing more than short exposure—cumulative energy damage), reducing volume by half reduces energy to 1/4 (50% quieter amplitude gives 25% energy, much safer); (2) wave power: ocean waves with 1 m amplitude have 100× more energy than 10 cm ripples ((100 cm / 10 cm)² = 10² = 100×), explaining why storm waves (large amplitude) are so destructive while calm ripples (small amplitude) are harmless—energy for moving/destroying objects proportional to amplitude squared. Understanding squared relationship helps: predict energy changes from amplitude changes (amplitude drops 30% → energy drops to 49%: 0.7² = 0.49), compare waves (one has 2× amplitude, other has 4× energy—can verify E ∝ A² relationship holds), and design for energy (want high energy wave? need large amplitude; want low energy? small amplitude suffices—squared relationship means amplitude control is powerful energy control).

This question tests understanding that wave energy is proportional to amplitude squared (E ∝ A²), meaning larger amplitude waves carry significantly more energy than smaller amplitude waves. The energy-amplitude relationship E ∝ A² creates dramatic effects: doubling amplitude quadruples energy (2× amplitude → 2² = 4× energy), tripling amplitude increases energy nine-fold (3× → 3² = 9×), and increasing amplitude by factor of 10 increases energy by factor of 100 (10× → 10² = 100×)—this squared relationship means small changes in amplitude produce large changes in energy, which explains why loud sounds (large amplitude) are so much more energetic than quiet sounds (small amplitude), why bright lights carry much more energy than dim lights, and why large ocean waves are so powerful compared to ripples (a 2 m wave has 10,000× more energy than a 2 cm ripple: (200 cm / 2 cm)² = 100² = 10,000). For comparing multiple waves: Given three waves with amplitudes 1 cm, 2 cm, and 3 cm, ranking by energy requires calculating E ∝ A² for each: 1 cm: E ∝ 1² = 1 (lowest, reference), 2 cm: E ∝ 2² = 4 (4× more than 1 cm), 3 cm: E ∝ 3² = 9 (9× more, highest)—energy ranking follows amplitude ranking (1 < 2 < 3 cm by amplitude gives 1 < 4 < 9 by energy), but energy differences are larger than amplitude differences (3 cm is 3× taller than 1 cm, but has 9× more energy). Observable consequences: the 3 cm wave (9× more energy) is much more powerful, can move larger objects, delivers more impact, while the 1 cm wave (less energy) disturbs water less, has smaller effects. Choice C is correct because it properly identifies wave with larger amplitude has more energy and ranks them accordingly. Choice A compares reversed: claims smaller amplitude has more energy when larger amplitude always has more (E ∝ A² with positive proportionality). The E ∝ A² relationship has important practical implications: (1) safety: doubling volume (amplitude) on speakers quadruples energy delivered to ears (2× amplitude → 4× energy, why prolonged loud music damages hearing more than short exposure—cumulative energy damage), reducing volume by half reduces energy to 1/4 (50% quieter amplitude gives 25% energy, much safer); (2) wave power: ocean waves with 1 m amplitude have 100× more energy than 10 cm ripples ((100 cm / 10 cm)² = 10² = 100×), explaining why storm waves (large amplitude) are so destructive while calm ripples (small amplitude) are harmless—energy for moving/destroying objects proportional to amplitude squared; (3) light energy: laser pointer (small amplitude, focused beam) vs LED flashlight (moderate amplitude, spread): for same amplitude, laser delivers concentrated energy (can burn if focused, all energy in small spot), while LED spreads energy over large area (safe, same amplitude but distributed)—amplitude determines total energy, concentration determines intensity at points; and (4) energy to produce: creating large amplitude waves requires lots of energy input (shake rope with 10 cm amplitude takes much more effort than 2 cm: (10/2)² = 25× more energy needed, muscles work harder for larger amplitude). Understanding squared relationship helps: predict energy changes from amplitude changes (amplitude drops 30% → energy drops to 49%: 0.7² = 0.49), compare waves (one has 2× amplitude, other has 4× energy—can verify E ∝ A² relationship holds), and design for energy (want high energy wave? need large amplitude; want low energy? small amplitude suffices—squared relationship means amplitude control is powerful energy control).

This question tests understanding that wave energy is proportional to amplitude squared (E ∝ A²), meaning larger amplitude waves carry significantly more energy than smaller amplitude waves. The energy-amplitude relationship E ∝ A² creates dramatic effects: doubling amplitude quadruples energy (2× amplitude → 2² = 4× energy), tripling amplitude increases energy nine-fold (3× → 3² = 9×), and increasing amplitude by factor of 10 increases energy by factor of 100 (10× → 10² = 100×)—this squared relationship means small changes in amplitude produce large changes in energy, which explains why loud sounds (large amplitude) are so much more energetic than quiet sounds (small amplitude), why bright lights carry much more energy than dim lights, and why large ocean waves are so powerful compared to ripples (a 2 m wave has 10,000× more energy than a 2 cm ripple: (200 cm / 2 cm)² = 100² = 10,000). For comparing two water waves: Initial amplitude 4 cm and new amplitude 6 cm differ in energy by the squared amplitude ratio: first calculate amplitude ratio (A_2/A_1 = 6 cm / 4 cm = 1.5, new wave has 1.5× larger amplitude), then square this ratio for energy comparison (E_2/E_1 = 1.5² = 2.25, new wave has 2.25× more energy than initial); the calculation shows that although the new wave is only 1.5× taller (amplitude 1.5× larger), it carries 2.25× more energy (squared effect: 1.5² = 2.25), demonstrating the E ∝ A² relationship—the larger amplitude means significantly more energy than amplitude ratio alone suggests (if energy were linear in amplitude, new wave would have only 1.5× more energy, but squared relationship gives 2.25×); observable consequences: new wave (2.25× more energy) is more powerful, can move larger objects, delivers more impact, while initial (less energy) disturbs slinky less, has smaller effects. Choice C is correct because it accurately calculates energy ratio by squaring amplitude ratio. Choice A uses linear relationship incorrectly: claims 1.5× amplitude gives 1.5× energy when E ∝ A² means 1.5² = 2.25× energy. The E ∝ A² relationship has important practical implications: (1) safety: doubling volume (amplitude) on speakers quadruples energy delivered to ears (2× amplitude → 4× energy, why prolonged loud music damages hearing more than short exposure—cumulative energy damage), reducing volume by half reduces energy to 1/4 (50% quieter amplitude gives 25% energy, much safer); (2) wave power: ocean waves with 1 m amplitude have 100× more energy than 10 cm ripples ((100 cm / 10 cm)² = 10² = 100×), explaining why storm waves (large amplitude) are so destructive while calm ripples (small amplitude) are harmless—energy for moving/destroying objects proportional to amplitude squared. Understanding squared relationship helps: predict energy changes from amplitude changes (amplitude drops 30% → energy drops to 49%: 0.7² = 0.49), compare waves (one has 2× amplitude, other has 4× energy—can verify E ∝ A² relationship holds), and design for energy (want high energy wave? need large amplitude; want low energy? small amplitude suffices—squared relationship means amplitude control is powerful energy control).

This question tests understanding that wave energy is proportional to amplitude squared (E ∝ A²), meaning larger amplitude waves carry significantly more energy than smaller amplitude waves. The energy-amplitude relationship E ∝ A² creates dramatic effects: doubling amplitude quadruples energy (2× amplitude → 2² = 4× energy), tripling amplitude increases energy nine-fold (3× → 3² = 9×), and increasing amplitude by factor of 10 increases energy by factor of 100 (10× → 10² = 100×)—this squared relationship means small changes in amplitude produce large changes in energy, which explains why loud sounds (large amplitude) are so much more energetic than quiet sounds (small amplitude), why bright lights carry much more energy than dim lights, and why large ocean waves are so powerful compared to ripples (a 2 m wave has 10,000× more energy than a 2 cm ripple: (200 cm / 2 cm)² = 100² = 10,000). For sound energy comparison: When amplitude is halved, the new amplitude is 0.5 times the original, so energy ratio is (0.5)² = 0.25 or 1/4, meaning the quieter sound has 1/4 the energy of the original; this dramatic drop (halving amplitude quarters energy) explains why turning down volume significantly reduces power consumption in speakers and protects hearing (less energy delivered to ears), and why small amplitude changes can make sounds much less intense. Choice B is correct because it accurately calculates energy ratio by squaring the amplitude ratio. Choice A uses linear relationship incorrectly: claims halving amplitude gives 1/2 energy when E ∝ A² means (0.5)² = 1/4 energy. The E ∝ A² relationship has important practical implications: (1) safety: doubling volume (amplitude) on speakers quadruples energy delivered to ears (2× amplitude → 4× energy, why prolonged loud music damages hearing more than short exposure—cumulative energy damage), reducing volume by half reduces energy to 1/4 (50% quieter amplitude gives 25% energy, much safer); (2) wave power: ocean waves with 1 m amplitude have 100× more energy than 10 cm ripples ((100 cm / 10 cm)² = 10² = 100×), explaining why storm waves (large amplitude) are so destructive while calm ripples (small amplitude) are harmless—energy for moving/destroying objects proportional to amplitude squared. Understanding squared relationship helps: predict energy changes from amplitude changes (amplitude drops 30% → energy drops to 49%: 0.7² = 0.49), compare waves (one has 2× amplitude, other has 4× energy—can verify E ∝ A² relationship holds), and design for energy (want high energy wave? need large amplitude; want low energy? small amplitude suffices—squared relationship means amplitude control is powerful energy control).

This question tests understanding that wave energy is proportional to amplitude squared (E ∝ A²), meaning larger amplitude waves carry significantly more energy than smaller amplitude waves. The energy-amplitude relationship E ∝ A² creates dramatic effects: doubling amplitude quadruples energy (2× amplitude → 2² = 4× energy), tripling amplitude increases energy nine-fold (3× → 3² = 9×), and increasing amplitude by factor of 10 increases energy by factor of 100 (10× → 10² = 100×)—this squared relationship means small changes in amplitude produce large changes in energy, which explains why loud sounds (large amplitude) are so much more energetic than quiet sounds (small amplitude), why bright lights carry much more energy than dim lights, and why large ocean waves are so powerful compared to ripples (a 2 m wave has 10,000× more energy than a 2 cm ripple: (200 cm / 2 cm)² = 100² = 10,000). For comparing two water waves: Wave 1 with amplitude 5 cm and Wave 2 with amplitude 10 cm differ in energy by the squared amplitude ratio: first calculate amplitude ratio (A_2/A_1 = 10 cm / 5 cm = 2, Wave 2 has 2× larger amplitude), then square this ratio for energy comparison (E_2/E_1 = 2² = 4, Wave 2 has 4× more energy than Wave 1); the calculation shows that although Wave 2 is only 2× taller (amplitude 2× larger), it carries 4× more energy (squared effect: 2² = 4), demonstrating the E ∝ A² relationship—the larger amplitude means significantly more energy than amplitude ratio alone suggests (if energy were linear in amplitude, Wave 2 would have only 2× more energy, but squared relationship gives 4×); observable consequences: Wave 2 (4× more energy) is much more powerful, can move larger objects, delivers more impact, while Wave 1 (less energy) disturbs the rope less, has smaller effects. Choice B is correct because it accurately calculates energy ratio by squaring amplitude ratio. Choice A uses linear relationship incorrectly: claims 2× amplitude gives 2× energy when E ∝ A² means 2² = 4× energy. The E ∝ A² relationship has important practical implications: (1) safety: doubling volume (amplitude) on speakers quadruples energy delivered to ears (2× amplitude → 4× energy, why prolonged loud music damages hearing more than short exposure—cumulative energy damage), reducing volume by half reduces energy to 1/4 (50% quieter amplitude gives 25% energy, much safer); (2) wave power: ocean waves with 1 m amplitude have 100× more energy than 10 cm ripples ((100 cm / 10 cm)² = 10² = 100×), explaining why storm waves (large amplitude) are so destructive while calm ripples (small amplitude) are harmless—energy for moving/destroying objects proportional to amplitude squared. Understanding squared relationship helps: predict energy changes from amplitude changes (amplitude drops 30% → energy drops to 49%: 0.7² = 0.49), compare waves (one has 2× amplitude, other has 4× energy—can verify E ∝ A² relationship holds), and design for energy (want high energy wave? need large amplitude; want low energy? small amplitude suffices—squared relationship means amplitude control is powerful energy control).

This question tests understanding that wave energy is proportional to amplitude squared (E ∝ A²), meaning larger amplitude waves carry significantly more energy than smaller amplitude waves. The energy-amplitude relationship E ∝ A² creates dramatic effects: doubling amplitude quadruples energy (2× amplitude → 2² = 4× energy), tripling amplitude increases energy nine-fold (3× → 3² = 9×), and increasing amplitude by factor of 10 increases energy by factor of 100 (10× → 10² = 100×)—this squared relationship means small changes in amplitude produce large changes in energy, which explains why loud sounds (large amplitude) are so much more energetic than quiet sounds (small amplitude), why bright lights carry much more energy than dim lights, and why large ocean waves are so powerful compared to ripples (a 2 m wave has 10,000× more energy than a 2 cm ripple: (200 cm / 2 cm)² = 100² = 10,000). For comparing two water waves: Gentle shake with amplitude 2 cm and hard shake with amplitude 8 cm differ in energy by the squared amplitude ratio: first calculate amplitude ratio (A_hard/A_gentle = 8 cm / 2 cm = 4, hard shake has 4× larger amplitude), then square this ratio for energy comparison (E_hard/E_gentle = 4² = 16, hard shake has 16× more energy than gentle); the calculation shows that although hard shake is only 4× taller (amplitude 4× larger), it carries 16× more energy (squared effect: 4² = 16), demonstrating the E ∝ A² relationship—the larger amplitude means significantly more energy than amplitude ratio alone suggests (if energy were linear in amplitude, hard shake would have only 4× more energy, but squared relationship gives 16×); observable consequences: hard shake (16× more energy) is much more powerful, can move larger objects, delivers more impact, while gentle (less energy) disturbs rope less, has smaller effects. Choice C is correct because it accurately calculates energy ratio by squaring amplitude ratio. Choice A uses linear relationship incorrectly: claims 4× amplitude gives 4× energy when E ∝ A² means 4² = 16× energy. The E ∝ A² relationship has important practical implications: (1) safety: doubling volume (amplitude) on speakers quadruples energy delivered to ears (2× amplitude → 4× energy, why prolonged loud music damages hearing more than short exposure—cumulative energy damage), reducing volume by half reduces energy to 1/4 (50% quieter amplitude gives 25% energy, much safer); (2) wave power: ocean waves with 1 m amplitude have 100× more energy than 10 cm ripples ((100 cm / 10 cm)² = 10² = 100×), explaining why storm waves (large amplitude) are so destructive while calm ripples (small amplitude) are harmless—energy for moving/destroying objects proportional to amplitude squared. Understanding squared relationship helps: predict energy changes from amplitude changes (amplitude drops 30% → energy drops to 49%: 0.7² = 0.49), compare waves (one has 2× amplitude, other has 4× energy—can verify E ∝ A² relationship holds), and design for energy (want high energy wave? need large amplitude; want low energy? small amplitude suffices—squared relationship means amplitude control is powerful energy control).

This question tests understanding that wave energy is proportional to amplitude squared (E ∝ A²), meaning larger amplitude waves carry significantly more energy than smaller amplitude waves. The energy-amplitude relationship E ∝ A² creates dramatic effects: doubling amplitude quadruples energy (2× amplitude → 2² = 4× energy), tripling amplitude increases energy nine-fold (3× → 3² = 9×), and increasing amplitude by factor of 10 increases energy by factor of 100 (10× → 10² = 100×)—this squared relationship means small changes in amplitude produce large changes in energy, which explains why loud sounds (large amplitude) are so much more energetic than quiet sounds (small amplitude), why bright lights carry much more energy than dim lights, and why large ocean waves are so powerful compared to ripples (a 2 m wave has 10,000× more energy than a 2 cm ripple: (200 cm / 2 cm)² = 100² = 10,000). For light brightness: Comparing dim light (small amplitude EM oscillation) to bright light (large amplitude 10× bigger), the energy difference is 10² = 100× (bright light carries 100× more energy per unit area than dim); this energy difference means: bright light can heat objects significantly (100× more energy absorbed warms materials), can damage eyes (intense light delivers too much energy to retina), requires much more power to produce (100 W bulb to produce bright vs 1 W LED for dim—power ratio matches energy ratio for same area), and can drive photosynthesis or chemical reactions faster (more photon energy available, more reactions per second). Choice C is correct because it accurately calculates energy ratio by squaring amplitude ratio. Choice A uses linear relationship incorrectly: claims 10× amplitude gives 10× energy when E ∝ A² means 10² = 100× energy. The E ∝ A² relationship has important practical implications: (1) safety: doubling volume (amplitude) on speakers quadruples energy delivered to ears (2× amplitude → 4× energy, why prolonged loud music damages hearing more than short exposure—cumulative energy damage), reducing volume by half reduces energy to 1/4 (50% quieter amplitude gives 25% energy, much safer); (2) wave power: ocean waves with 1 m amplitude have 100× more energy than 10 cm ripples ((100 cm / 10 cm)² = 10² = 100×), explaining why storm waves (large amplitude) are so destructive while calm ripples (small amplitude) are harmless—energy for moving/destroying objects proportional to amplitude squared. Understanding squared relationship helps: predict energy changes from amplitude changes (amplitude drops 30% → energy drops to 49%: 0.7² = 0.49), compare waves (one has 2× amplitude, other has 4× energy—can verify E ∝ A² relationship holds), and design for energy (want high energy wave? need large amplitude; want low energy? small amplitude suffices—squared relationship means amplitude control is powerful energy control).

This question tests understanding that wave energy is proportional to amplitude squared (E ∝ A²), meaning larger amplitude waves carry significantly more energy than smaller amplitude waves. The energy-amplitude relationship E ∝ A² creates dramatic effects: doubling amplitude quadruples energy (2× amplitude → 2² = 4× energy), tripling amplitude increases energy nine-fold (3× → 3² = 9×), and increasing amplitude by factor of 10 increases energy by factor of 100 (10× → 10² = 100×)—this squared relationship means small changes in amplitude produce large changes in energy, which explains why loud sounds (large amplitude) are so much more energetic than quiet sounds (small amplitude), why bright lights carry much more energy than dim lights, and why large ocean waves are so powerful compared to ripples (a 2 m wave has 10,000× more energy than a 2 cm ripple: (200 cm / 2 cm)² = 100² = 10,000). For comparing two water waves: Wave A with amplitude 2 cm and Wave B with amplitude 6 cm differ in energy by the squared amplitude ratio: first calculate amplitude ratio (A_B/A_A = 6 cm / 2 cm = 3, Wave B has 3× larger amplitude), then square this ratio for energy comparison (E_B/E_A = 3² = 9, Wave B has 9× more energy than Wave A); the calculation shows that although Wave B is only 3× taller (amplitude 3× larger), it carries 9× more energy (squared effect: 3² = 9), demonstrating the E ∝ A² relationship—the larger amplitude means significantly more energy than amplitude ratio alone suggests (if energy were linear in amplitude, Wave B would have only 3× more energy, but squared relationship gives 9×); observable consequences: Wave B (9× more energy) is much more powerful, can move larger objects, delivers more impact, while Wave A (less energy) disturbs water less, has smaller effects. Choice C is correct because it accurately calculates energy ratio by squaring amplitude ratio. Choice A uses linear relationship incorrectly: claims 3× amplitude gives 3× energy when E ∝ A² means 3² = 9× energy. The E ∝ A² relationship has important practical implications: (1) safety: doubling volume (amplitude) on speakers quadruples energy delivered to ears (2× amplitude → 4× energy, why prolonged loud music damages hearing more than short exposure—cumulative energy damage), reducing volume by half reduces energy to 1/4 (50% quieter amplitude gives 25% energy, much safer); (2) wave power: ocean waves with 1 m amplitude have 100× more energy than 10 cm ripples ((100 cm / 10 cm)² = 10² = 100×), explaining why storm waves (large amplitude) are so destructive while calm ripples (small amplitude) are harmless—energy for moving/destroying objects proportional to amplitude squared. Understanding squared relationship helps: predict energy changes from amplitude changes (amplitude drops 30% → energy drops to 49%: 0.7² = 0.49), compare waves (one has 2× amplitude, other has 4× energy—can verify E ∝ A² relationship holds), and design for energy (want high energy wave? need large amplitude; want low energy? small amplitude suffices—squared relationship means amplitude control is powerful energy control).

This question tests understanding that wave energy is proportional to amplitude squared (E ∝ A²), meaning larger amplitude waves carry significantly more energy than smaller amplitude waves. The energy-amplitude relationship E ∝ A² creates dramatic effects: doubling amplitude quadruples energy (2× amplitude → 2² = 4× energy), tripling amplitude increases energy nine-fold (3× → 3² = 9×), and increasing amplitude by factor of 10 increases energy by factor of 100 (10× → 10² = 100×)—this squared relationship means small changes in amplitude produce large changes in energy, which explains why loud sounds (large amplitude) are so much more energetic than quiet sounds (small amplitude), why bright lights carry much more energy than dim lights, and why large ocean waves are so powerful compared to ripples (a 2 m wave has 10,000× more energy than a 2 cm ripple: (200 cm / 2 cm)² = 100² = 10,000). For sound energy comparison: A quiet sound with pressure amplitude 5 Pa compared to a loud sound with amplitude 50 Pa shows dramatic energy difference: amplitude ratio is 50/5 = 10 (loud sound has 10× larger amplitude), and energy ratio is 10² = 100 (loud sound has 100× more energy than quiet sound); this 100-fold energy difference explains why loud sounds can damage hearing (delivering 100× more energy to ear structures at high amplitude compared to quiet sounds), why loud sounds can be felt (vibrations transfer significant energy to body), and why sound systems require much more power for high volume (producing large amplitude requires lots of energy input: 100× more energy needed for 10× louder amplitude). Choice C is correct because it accurately calculates energy ratio by squaring amplitude ratio. Choice A uses linear relationship incorrectly: claims 10× amplitude gives 10× energy when E ∝ A² means 10² = 100× energy. The E ∝ A² relationship has important practical implications: (1) safety: doubling volume (amplitude) on speakers quadruples energy delivered to ears (2× amplitude → 4× energy, why prolonged loud music damages hearing more than short exposure—cumulative energy damage), reducing volume by half reduces energy to 1/4 (50% quieter amplitude gives 25% energy, much safer); (2) wave power: ocean waves with 1 m amplitude have 100× more energy than 10 cm ripples ((100 cm / 10 cm)² = 10² = 100×), explaining why storm waves (large amplitude) are so destructive while calm ripples (small amplitude) are harmless—energy for moving/destroying objects proportional to amplitude squared. Understanding squared relationship helps: predict energy changes from amplitude changes (amplitude drops 30% → energy drops to 49%: 0.7² = 0.49), compare waves (one has 2× amplitude, other has 4× energy—can verify E ∝ A² relationship holds), and design for energy (want high energy wave? need large amplitude; want low energy? small amplitude suffices—squared relationship means amplitude control is powerful energy control).

This question tests understanding that wave energy is proportional to amplitude squared (E ∝ A²), meaning larger amplitude waves carry significantly more energy than smaller amplitude waves. The energy-amplitude relationship E ∝ A² creates dramatic effects: doubling amplitude quadruples energy (2× amplitude → 2² = 4× energy), tripling amplitude increases energy nine-fold (3× → 3² = 9×), and increasing amplitude by factor of 10 increases energy by factor of 100 (10× → 10² = 100×)—this squared relationship means small changes in amplitude produce large changes in energy, which explains why loud sounds (large amplitude) are so much more energetic than quiet sounds (small amplitude), why bright lights carry much more energy than dim lights, and why large ocean waves are so powerful compared to ripples (a 2 m wave has 10,000× more energy than a 2 cm ripple: (200 cm / 2 cm)² = 100² = 10,000). For comparing two water waves: Wave X with amplitude 3 cm and Wave Y with amplitude 1 cm differ in energy by the squared amplitude ratio: first calculate amplitude ratio (A_X/A_Y = 3 cm / 1 cm = 3, Wave X has 3× larger amplitude), then square this ratio for energy comparison (E_X/E_Y = 3² = 9, Wave X has 9× more energy than Wave Y); the calculation shows that although Wave X is only 3× taller (amplitude 3× larger), it carries 9× more energy (squared effect: 3² = 9), demonstrating the E ∝ A² relationship—the larger amplitude means significantly more energy than amplitude ratio alone suggests (if energy were linear in amplitude, Wave X would have only 3× more energy, but squared relationship gives 9×); observable consequences: Wave X (9× more energy) is much more powerful, can move larger objects, delivers more impact, while Wave Y (less energy) disturbs water less, has smaller effects. Choice B is correct because it accurately calculates energy ratio by squaring amplitude ratio. Choice A uses linear relationship incorrectly: claims 3× amplitude gives 3× energy when E ∝ A² means 3² = 9× energy. The E ∝ A² relationship has important practical implications: (1) safety: doubling volume (amplitude) on speakers quadruples energy delivered to ears (2× amplitude → 4× energy, why prolonged loud music damages hearing more than short exposure—cumulative energy damage), reducing volume by half reduces energy to 1/4 (50% quieter amplitude gives 25% energy, much safer); (2) wave power: ocean waves with 1 m amplitude have 100× more energy than 10 cm ripples ((100 cm / 10 cm)² = 10² = 100×), explaining why storm waves (large amplitude) are so destructive while calm ripples (small amplitude) are harmless—energy for moving/destroying objects proportional to amplitude squared. Understanding squared relationship helps: predict energy changes from amplitude changes (amplitude drops 30% → energy drops to 49%: 0.7² = 0.49), compare waves (one has 2× amplitude, other has 4× energy—can verify E ∝ A² relationship holds), and design for energy (want high energy wave? need large amplitude; want low energy? small amplitude suffices—squared relationship means amplitude control is powerful energy control).