Book cover for Applied Physics

Applied Physics

Dale Ewen, Neil Schurter, P. Erik Gundersen

ISBN #9780134159386

11th Edition

2,119 Questions

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18,063 Students Helped

Homework Questions

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Summary
Learning Objectives
Key Concepts
Example Problems
Explanations
Common Mistakes

Summary

This section highlights the importance of the speed of light as a fundamental constant in physics and its applications across science and engineering. It explains how early scientists like Ole Roemer and Albert Michelson developed methods to measure this speed. The relationship s = ct is central in calculating distances for various electromagnetic waves, and the discussion on light as a wave covers both its wavelength and frequency, which dictate observable properties such as color. These principles have profound applications in fields ranging from astronomy to modern surveying.

Learning Objectives

1

Understand the significance of the speed of light and its measurement methods (Roemer’s eclipse timing and Michelson’s rotating mirror technique).

2

Apply the equation s = ct to calculate distances traveled by various forms of electromagnetic radiation.

3

Describe the wave characteristics of light, including wavelength and frequency, and how these relate to color perception.

4

Analyze real-world applications, such as astronomical distance measurements (using light years) and surveying techniques using electromagnetic signals.

Key Concepts

CONCEPT

DEFINITION

Speed of Light

The constant speed at which light and all electromagnetic radiation travel in a vacuum, defined as 299,792,458 m/s (approximately 3.00 x 10^8 m/s or 186,000 mi/s).

Electromagnetic Radiation

Forms of energy propagation that include light, radio waves, infrared, ultraviolet, X-rays, and gamma rays, characterized by oscillating electric and magnetic fields.

s = ct

The equation used to calculate the distance (s) traveled by electromagnetic radiation, where c is the speed of light and t is the time.

Wavelength (λ)

The distance between two successive corresponding points on a wave, such as the distance between peaks; determines the color of visible light.

Frequency (f)

The number of cycles or vibrations of a wave per second, measured in Hertz (Hz); higher frequencies correspond to shorter wavelengths in the electromagnetic spectrum.

Light-year

The distance traveled by light in one Earth year, used to express astronomical distances (approximately 5.87 x 10^12 miles or 9.45 x 10^15 meters).

Interferometer

An instrument that uses the interference of light waves to make precise measurements, such as determining a star's diameter.

Example Problems

Example 1

Find the distance (in metres) traveled by a radio wave in $5.00 \mathrm{~s}$.

Example 2

Find the distance (in metres) traveled by a light wave in $6.40 \mathrm{~s}$.

Example 3

A television signal is sent to a communications satellite that is $20, \overline{0} 00$ mi above a relay station. How long does it take for the signal to reach the satellite?

Example 4

How long does it take for a radio signal from the earth to reach an astronaut on the moon? The distance from the earth to the moon is $2.40 \times 10^{5} \mathrm{mi}$.

Example 5

The sun is $9.30 \times 10^{7}$ mi from the earth. How long does it take light to travel from the sun to the earth?
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Step-by-Step Explanations

QUESTION

Find the distance (in miles) traveled by an X ray in 0.100 s given that the speed of light is 186,000 mi/s.

STEP-BY-STEP ANSWER:

Step 1: Identify the formula for distance: s = ct.
Step 2: Substitute the given speed (c = 186,000 mi/s) and time (t = 0.100 s) into the formula.
Step 3: Calculate the distance: s = (186,000 mi/s) * (0.100 s) = 18,600 mi.
Final Answer: The X ray travels 18,600 miles in 0.100 seconds.

Distance traveled by an X ray

QUESTION

Find the distance (in meters) traveled by a radio wave in 5.00 s, given the speed of light as 3.00 x 10^8 m/s.

STEP-BY-STEP ANSWER:

Step 1: Use the equation s = ct.
Step 2: Substitute c = 3.00 x 10^8 m/s and t = 5.00 s.
Step 3: Multiply the values: s = (3.00 x 10^8 m/s) * (5.00 s) = 1.50 x 10^9 m.
Final Answer: The radio wave travels 1.50 x 10^9 meters in 5.00 seconds.

Distance traveled by a radio wave

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Common Mistakes

  • Confusing the units for distance, time, and speed, which can lead to incorrect calculations.
  • Assuming that the speed of light varies in all circumstances, without recognizing that it is constant in a vacuum.
  • Mixing up the concepts of wavelength and frequency: longer wavelengths correspond to lower frequencies and vice versa.
  • Overlooking the importance of precision in measurement methods such as those developed by Michelson, especially when calculating large astronomical distances.