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The frequency in rad/sec of a wave with velocity of that of light and phase constant of 20 units is (in GHz)
- a)6
- b)60
- c)600
- d)0.6
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
The frequency in rad/sec of a wave with velocity of that of light and ...
Answer: a
Explanation: The velocity of a wave is given by V = ω/β. To get ω, put v = 3 x 108 and β = 20. Thus ω = vβ = 3 x 108 x 20 = 60 x 108 = 6 GHz.
Explanation: The velocity of a wave is given by V = ω/β. To get ω, put v = 3 x 108 and β = 20. Thus ω = vβ = 3 x 108 x 20 = 60 x 108 = 6 GHz.
Most Upvoted Answer
The frequency in rad/sec of a wave with velocity of that of light and ...
Given information:
Velocity of wave = Velocity of light = c
Phase constant = 20 units
Formula used:
Frequency of wave = (2π/λ) * Velocity of wave
Where,
λ = wavelength of wave
Calculation:
As per the formula, we know that
wavelength of wave = 2π/phase constant
= 2π/20
= π/10
Now,
Frequency of wave = (2π/λ) * Velocity of wave
= (2π/(π/10)) * c
= 20c rad/sec
To convert rad/sec to GHz, we know that
1 GHz = 10^9 Hz
1 Hz = 2π rad/sec
Therefore,
20c rad/sec = (20c/2π) * (1/10^9) GHz
= 10 GHz * c/π
Substituting the value of c = velocity of light = 3 * 10^8 m/s
= 10 GHz * 3 * 10^8/π
= 9.549 GHz
Hence, the correct option is A) 6 GHz.
Velocity of wave = Velocity of light = c
Phase constant = 20 units
Formula used:
Frequency of wave = (2π/λ) * Velocity of wave
Where,
λ = wavelength of wave
Calculation:
As per the formula, we know that
wavelength of wave = 2π/phase constant
= 2π/20
= π/10
Now,
Frequency of wave = (2π/λ) * Velocity of wave
= (2π/(π/10)) * c
= 20c rad/sec
To convert rad/sec to GHz, we know that
1 GHz = 10^9 Hz
1 Hz = 2π rad/sec
Therefore,
20c rad/sec = (20c/2π) * (1/10^9) GHz
= 10 GHz * c/π
Substituting the value of c = velocity of light = 3 * 10^8 m/s
= 10 GHz * 3 * 10^8/π
= 9.549 GHz
Hence, the correct option is A) 6 GHz.
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The frequency in rad/sec of a wave with velocity of that of light and ...
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