Which of the following statements) is/are TRUE?a)The phase velocity of a wave can never be higher than the speed of light.b)The group velocity of a wave can never be higher than the speed of light.c)Both the group and phase velocities of a wave can never be higher than the speed of light.d)There is no such limits on either the group or the phase velocities of a wave.Correct answer is option 'B'. Can you explain this answer?

Question

Answer

Explanation:

Group Velocity:
The group velocity of a wave is the velocity at which the overall shape or envelope of the wave propagates through space. It is related to the rate of energy transfer in the wave.

Phase Velocity:
The phase velocity of a wave is the velocity at which the phase of the wave propagates through space. It represents the speed at which individual crests or troughs of the wave move.

Speed of Light:
The speed of light in vacuum is a fundamental constant of nature and is denoted by 'c'. Its value is approximately 3 x 10^8 meters per second.

Statement a: The phase velocity of a wave can never be higher than the speed of light.
This statement is true. According to the theory of relativity, the speed of light is the maximum speed at which information or energy can be transmitted. Thus, the phase velocity of a wave cannot exceed the speed of light.

Statement b: The group velocity of a wave can never be higher than the speed of light.
This statement is also true. The group velocity is related to the phase velocity and the wavelength of the wave. Since the phase velocity cannot exceed the speed of light, the group velocity also cannot exceed the speed of light.

Statement c: Both the group and phase velocities of a wave can never be higher than the speed of light.
This statement is incorrect. While the group and phase velocities are related, they are not the same. The phase velocity represents the speed of individual crests or troughs, while the group velocity represents the speed of the overall envelope. It is possible for the phase velocity to be equal to or less than the speed of light, while the group velocity can be higher than the speed of light.

Statement d: There is no such limits on either the group or the phase velocities of a wave.
This statement is false. As explained earlier, both the group and phase velocities of a wave cannot exceed the speed of light. The theory of relativity sets a fundamental limit on the speed at which information or energy can be transmitted.

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