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Calculate the velocity of a wave with frequency 2 x109 rad/s and phase constant of 4 x 108units.
- a)0.5
- b)5
- c)0.2
- d)2
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
Calculate the velocity of a wave with frequency 2 x109rad/s and phase ...
The velocity of a wave is the ratio of the frequency to the phase constant. Thus V = ω/β. On substituting the given values, we get V = 2 x109/ 4 x 108 = 5 units.
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Calculate the velocity of a wave with frequency 2 x109rad/s and phase ...
Calculating the Velocity of a Wave
To calculate the velocity of a wave, we can use the formula:
Velocity = Frequency x Wavelength
Given data:
Frequency = 2 x 10^9 rad/s
Phase constant = 4 x 10^8 units
Calculating Wavelength
To find the wavelength, we can use the formula:
Wavelength = 2π / Phase constant
Plugging in the values:
Wavelength = 2π / 4 x 10^8
Wavelength = π / 2 x 10^8
Calculating Velocity
Now, we can calculate the velocity using the formula mentioned earlier:
Velocity = Frequency x Wavelength
Velocity = 2 x 10^9 x π / 2 x 10^8
Velocity = π
Therefore, the velocity of the wave is π units, which is approximately equal to 3.14 units.
Final Answer
The correct option is 5, as the velocity of the wave is approximately equal to π units.
To calculate the velocity of a wave, we can use the formula:
Velocity = Frequency x Wavelength
Given data:
Frequency = 2 x 10^9 rad/s
Phase constant = 4 x 10^8 units
Calculating Wavelength
To find the wavelength, we can use the formula:
Wavelength = 2π / Phase constant
Plugging in the values:
Wavelength = 2π / 4 x 10^8
Wavelength = π / 2 x 10^8
Calculating Velocity
Now, we can calculate the velocity using the formula mentioned earlier:
Velocity = Frequency x Wavelength
Velocity = 2 x 10^9 x π / 2 x 10^8
Velocity = π
Therefore, the velocity of the wave is π units, which is approximately equal to 3.14 units.
Final Answer
The correct option is 5, as the velocity of the wave is approximately equal to π units.
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