Elaborate on the difference between the energy of the two waves seen here:
(1 point)
Responses
Wave energy is directly proportional to frequency and wavelength, therefore Wave A has more energy.
Wave energy is directly proportional to frequency and wavelength, therefore Wave A has more energy.
Wave A has more energy than Wave B because the wavelength of Wave A is greater.
Wave A has more energy than Wave B because the wavelength of Wave A is greater.
Wave B has more energy than Wave A because the frequency of Wave B is greater.
Wave B has more energy than Wave A because the frequency of Wave B is greater.
Wave B has more energy: the amplitude of Wave B is double that of Wave A.
All Answers 1
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GPT-5 mini
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Correct choice: "Wave B has more energy: the amplitude of Wave B is double that of Wave A."
Why: For waves the energy carried is proportional to the square of the amplitude. So if Wave B's amplitude is twice Wave A's, its energy is (2)² = 4 times larger.
A bit more detail/caveats:
- For mechanical waves on a string or sound waves, average energy (or intensity) ∝ A² (and can also scale with ω² if frequencies differ).
- For electromagnetic waves the intensity is also ∝ (field amplitude)²; for photons the energy of each photon is ∝ frequency (E = hf), but the total energy flux depends on photon number (which relates to amplitude/intensity).
- The statement "energy is directly proportional to frequency and wavelength" is incorrect (for photons energy ∝ frequency and inversely ∝ wavelength; for classical waves amplitude is the primary factor).
Why: For waves the energy carried is proportional to the square of the amplitude. So if Wave B's amplitude is twice Wave A's, its energy is (2)² = 4 times larger.
A bit more detail/caveats:
- For mechanical waves on a string or sound waves, average energy (or intensity) ∝ A² (and can also scale with ω² if frequencies differ).
- For electromagnetic waves the intensity is also ∝ (field amplitude)²; for photons the energy of each photon is ∝ frequency (E = hf), but the total energy flux depends on photon number (which relates to amplitude/intensity).
- The statement "energy is directly proportional to frequency and wavelength" is incorrect (for photons energy ∝ frequency and inversely ∝ wavelength; for classical waves amplitude is the primary factor).
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