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Chapter 33: Problem 4

Does relativity require that the speed of sound be the same for all observers? Why or why not?

Short Answer

Expert verified
No, relativity does not require the speed of sound to be the same for all observers, as the speed of sound is not a universal constant and varies based on the medium it's passing through.

Step by step solution

01

Understanding Relativity

Relativity in Physics consists of two theories proposed by Albert Einstein: The Special Theory of Relativity and the General Theory of Relativity. The special theory of relativity states that the laws of physics are invariant (i.e., identical) in all inertial systems (i.e., non-accelerating frames of reference). It also states that the speed of light in a vacuum is the same for all observers, regardless of the motion of the light source.
02

Understanding Speed of Sound

The speed of sound depends on the medium through which the sound waves are passing. It's not a universal constant like the speed of light. It varies with the medium (air, water, steel etc.), temperature, pressure and humidity.
03

Differentiating Speed of Light and Sound

Unlike light, sound requires a medium to travel through, so its speed changes based on the properties of the medium. In relativity, the speed of light is constant for different observers due to the way spacetime is structured, but sound doesn't share the same principle due to its dependence on the medium.
04

Conclusion

Relativity does not require the speed of sound to be the same for all observers. This is due to the disparity between sound and light; the fact that light is a universal constant and sound is not.

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Most popular questions from this chapter

Two distant galaxies are receding from Earth at \(0.75 c\) in opposite directions. How fast does an observer in one galaxy measure the other to be moving?

You're writing a galactic history involving two civilizations that evolve on opposite sides of a \(1.0 \times 10^{5}\) -ly-diameter galaxy. In the galaxy's reference frame, civilization B launched its first spacecraft 45,000 years after civilization A. You and your readers, from a more advanced civilization, are traveling through the galaxy at \(0.99 c\) on a line from \(\mathrm{A}\) to \(\mathrm{B}\). Which civilization do you record as having first achieved interstellar travel, and how much in advance of the other?

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You've been named captain of NASA's first interstellar mission since the Voyager robotic spacecraft. You board your spaceship. accelerate quickly to \(0.8 c,\) and cruise at constant speed toward Proxima Centauri, the closest star to our Sun. Proxima Centauri is 4 light-years distant as measured in the two stars' common rest frame. On the way, you conduct various medical experiments to determine the effects of a long space voyage on the human body. In your spaceship's reference frame, the distance from the Sun to Proxima Centauri is a. 2.4 light years. b. just under 4 light years. c. 4 light years. d. 5 light years.

You've been named captain of NASA's first interstellar mission since the Voyager robotic spacecraft. You board your spaceship. accelerate quickly to \(0.8 c,\) and cruise at constant speed toward Proxima Centauri, the closest star to our Sun. Proxima Centauri is 4 light-years distant as measured in the two stars' common rest frame. On the way, you conduct various medical experiments to determine the effects of a long space voyage on the human body. Back on Earth, Mission Control judges that your shipboard clocks run slow. What do you judge about clocks at Mission Control? a. They run fast. b. They keep time at the same rate as your clocks. c. They run slow. d. You can't tell anything about their clocks.
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