Chapter 5: Problem 4

When a boat moves through the water, the waves in front of the boat bunch up, while the waves behind the boat spread out. This is an example of a. the Bohr model. b. the wave nature of light. c. emission and absorption. d. the Doppler effect.

Short Answer

Expert verified

d. the Doppler effect.

Step by step solution

Identify the Scenario

Analyze the situation described in the question – waves in front of the boat bunching up and waves behind the boat spreading out.

Recall Relevant Concepts

Remember the key concepts related to wave behavior, especially when an object is moving through a medium. This includes the Doppler effect, which describes changes in wave frequencies relative to the motion of the source.

Exclude Irrelevant Options

Evaluate each option: a. the Bohr model relates to atomic structure, b. the wave nature of light concerns light behaving as waves, c. emission and absorption are processes in which energy is absorbed or emitted by objects.

Confirm the Correct Concept

Conclude that the Doppler effect, related to changes in wave frequency or wavelength due to movement of a source relative to an observer, matches the description of waves bunching up in front and spreading out behind a moving boat.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Wave Behavior

Wave behavior is essential to comprehend many physical phenomena, including the Doppler effect. Waves propagate through different mediums (like water, air, etc.) and can exhibit various behaviors, such as reflection, refraction, diffraction, and interference.
When a boat moves through water, the water waves in front of it pile up, creating higher wave crests, while the waves behind it spread out, forming lower crests. This interaction signifies how waves behave when influenced by the motion of an object through a medium.
Key Points:

Waves can be mechanical (such as water waves) or electromagnetic (like light waves).
The way waves travel depends on the properties of the medium they are moving through.
When an object moves through a medium, it can alter the wave patterns, demonstrating the dynamic nature of wave behavior.

Understanding these basic properties helps in grasping more complex phenomena, such as the Doppler effect.

Wave Frequency and the Doppler Effect

Wave frequency refers to the number of wave cycles that pass a point per unit time. It's an integral part of wave behavior, influencing how we perceive waves.
The Doppler effect is a phenomenon that significantly affects wave frequency. It occurs when a wave source moves relative to an observer.
For instance:

When a boat sails through water, the waves in front of it get compressed, leading to a higher frequency.
Conversely, the waves behind it get stretched out, resulting in a lower frequency.

This change in frequency due to the relative motion is precisely what the Doppler effect explains. Here’s the general formula illustrating the Doppler effect in waves: The observed frequency \(\( f' \)\) is given by \(f' = \frac{f (v + v_o)}{(v - v_s)}\) where:

\(f\) is the emitted frequency,
\(v\) is the speed of the wave in the medium,
\(v_o\) is the velocity of the observer relative to the medium,
\(v_s\) is the velocity of the source relative to the medium.

This principle applies to various waves, including sound and light, indicating its broad significance in physics.

Motion in Medium and Its Influence on Waves

Motion in a medium can dramatically affect wave propagation. Whether it’s a boat moving through water or a vehicle moving through air, these movements alter the wave patterns in distinctive ways.
For water waves:

A boat cutting through water causes wave fronts to bunch up in front due to the compression of wave peaks.
Behind the boat, the waves spread out because of the stretching of wave troughs.

This behavior is observable in various scenarios, like when an ambulance speeds past us and the siren’s pitch changes.
Key Concepts:

The relative speed and direction of the source and observer determine how wave properties such as frequency and wavelength change.
Understanding these changes helps in applications ranging from radar technology to astronomical observations.

This fundamental understanding assists in more advanced studies, like sound waves, where similar principles measure speeds and distances, enhancing navigational and communicational technologies.

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When a boat moves through the water, the waves in front of the boat bunch up, while the waves behind the boat spread out. This is an example of a. the Bohr model. b. the wave nature of light. c. emission and absorption. d. the Doppler effect.

Short Answer

Step by step solution

Identify the Scenario

Recall Relevant Concepts

Exclude Irrelevant Options

Confirm the Correct Concept

Key Concepts

Understanding Wave Behavior

Wave Frequency and the Doppler Effect

Motion in Medium and Its Influence on Waves

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