Question

Wave A is traveling at a speed of 217 m/s and has a wavelength of 1.5m. Wave B is traveling at a speed of 500 m/s and has a wavelength of 2.5m. Which wave is carrying more energy? How do you know? (Assume amplitude is the same)

Answer 1

Wave B is carrying more energy. The frequency of Wave B is higher than that of Wave A, resulting in a greater energy.

Step-by-step explanation:

To determine which wave is carrying more energy, we can use the formula E = hf, where E is the energy, h is Planck's constant, and f is the frequency. Since the wavelength and amplitude are the same for both waves, we can calculate the frequency using the formula v = λf, where v is the speed of the wave and λ is the wavelength.

For Wave A: v = 217 m/s and λ = 1.5m, so f = v/λ = 217/1.5 = 144.67 Hz.

For Wave B: v = 500 m/s and λ = 2.5m, so f = v/λ = 500/2.5 = 200 Hz.

Now, calculating the energy using the formula E = hf:

For Wave A: E = (6.63 × 10^-34 J·s)(144.67 Hz) = 9.57 × 10^-33 J.

For Wave B: E = (6.63 × 10^-34 J·s)(200 Hz) = 1.33 × 10^-32 J.

Therefore, Wave B is carrying more energy as it has an energy of 1.33 × 10^-32 J compared to Wave A's energy of 9.57 × 10^-33 J.