Unit 14: Waves , Sound , and Physical Optics
Weightage : 15–18%
An astronaut in a rocket is passing by a space station at a velocity of \(0.33c\). Looking out the window, the astronaut sees a scientist on the space station fire a laser at a target. The laser is pointed in the same direction that the astronaut is traveling.
On which of the following observations will the astronaut and scientist agree?
Correct Answer: \( \boxed{\mathrm{C}} \)
According to Einstein’s theory of special relativity, the speed of light in a vacuum is the same for all inertial observers, regardless of the relative motion of the source or the observer.
\( c=3.0\times10^8\,\mathrm{m/s} \)
Although observers moving relative to one another may disagree about measured lengths (length contraction) and time intervals (time dilation), they will always measure the same value for the speed of light.
Therefore, both the astronaut and the scientist will measure the laser beam to travel at speed \(c\).
Therefore, the correct answer is (C).
A supernova explosion occurs at a distance of \(2\times10^{20}\,\mathrm{m}\) from Earth. The supernova simultaneously emits radiation at both visible and x-ray wavelengths.
Which of the following statements best describes the time it takes for the two types of radiation from the supernova to reach Earth?
Correct Answer: \( \boxed{\mathrm{B}} \)
Visible light and x-rays are both electromagnetic waves. In a vacuum, all electromagnetic waves travel at the same speed:
\( c=3.0\times10^{8}\,\mathrm{m/s} \)
The travel time is
\( t=\dfrac{d}{c}=\dfrac{2\times10^{20}}{3.0\times10^{8}}\approx6.7\times10^{11}\,\mathrm{s}\approx2.1\times10^{4}\,\mathrm{years} \)
Since both types of radiation travel at the same speed in space, they arrive at Earth simultaneously, even though they have different wavelengths and frequencies.
Therefore, the correct answer is (B).
The figure above shows a model of an electromagnetic wave, where \(E\) is the electric field and \(B\) is the magnetic field. In what direction is the energy of the wave transmitted?
Correct Answer: \( \boxed{\mathrm{A}} \)
Electromagnetic waves are transverse waves, meaning that the electric field, magnetic field, and direction of propagation are all mutually perpendicular.
In the figure:
• The electric field \(E\) oscillates along the y-axis.
• The magnetic field \(B\) oscillates along the z-axis.
The direction of energy transfer is given by the Poynting vector,
\( \displaystyle \vec{S}=\frac{1}{\mu_{0}}\left(\vec{E}\times\vec{B}\right). \)
Applying the right-hand rule to \( \vec{E}\times\vec{B} \), the energy propagates in the positive x-direction.
Therefore, the electromagnetic wave transmits energy along the x-axis only.
Therefore, the correct answer is (A).
