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Difficulty: Very hardWaves, Sound, and Light

A sensor hovering above a lake simultaneously emits a sound wave and a beam of monochromatic light downward into the water. As both waves transition from the air into the water, which of the following accurately describes the changes in their respective wave properties?

  1. The sound wave's speed and wavelength increase, while the light wave's speed and wavelength decrease; the frequency of both waves remains constant.Answer
  2. B
    Both waves experience a decrease in speed and a corresponding decrease in wavelength, while the frequency of both waves remains constant.
  3. C
    The sound wave's speed decreases and its frequency increases, while the light wave's speed increases and its frequency decreases.
  4. D
    The sound wave's speed and frequency increase, while the light wave's speed and frequency decrease; the wavelength of both waves remains constant.

Answer

The sound wave's speed and wavelength increase, while the light wave's speed and wavelength decrease; the frequency of both waves remains constant.
When any wave crosses a boundary between two media, its frequency remains constant because the number of cycles per second is locked to the original source. Sound is a mechanical wave and travels faster in water than in air because water is denser and more rigid. According to the wave equation (v=fλv = f \lambda), if speed (vv) increases and frequency (ff) is constant, wavelength (λ\lambda) must increase. Conversely, light is an electromagnetic wave that interacts with the atoms in the water, causing its propagation speed to decrease compared to its speed in air. Therefore, with a lower speed and constant frequency, the light wave's wavelength must decrease.

Step-by-Step Solution

1
Analyze the change in frequency for both waves.
The frequency of both the sound wave and the light wave remains constant.
Frequency is determined exclusively by the wave source and does not change when transitioning between different media.
2
Determine how the speed of each wave changes when moving from air to water.
The sound wave speeds up, while the light wave slows down.
Sound is a mechanical wave that requires a medium and travels faster in denser, less compressible materials (water > air). Light is an electromagnetic wave that is impeded by matter, so its speed decreases in media with higher optical density (water < air).
3
Apply the wave equation (v=fλv = f \lambda) to determine wavelength changes.
The sound wave's wavelength increases, and the light wave's wavelength decreases.
Because frequency (ff) is constant, wavelength (λ\lambda) must change directly proportionally to wave speed (vv). Higher speed means longer wavelength; lower speed means shorter wavelength.

Key Concept

Wave Propagation Across Boundaries
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Topics

Waves, Sound, and Light

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