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Find the guided wavelength if the distance between the two conducting plates in the waveguide is 2 cm.
- a)4cm
- b)2cm
- c)1cm
- d)0.5cm
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
Find the guided wavelength if the distance between the two conducting ...
Answer: a
Explanation: The distance between the terminating plates is given by Vmin = λg/2, where λg is the guided wavelength. On substituting for Vmin = 2cm, we get λg = 2Vmin = 2 x 0.02 = 4cm.
Explanation: The distance between the terminating plates is given by Vmin = λg/2, where λg is the guided wavelength. On substituting for Vmin = 2cm, we get λg = 2Vmin = 2 x 0.02 = 4cm.
Most Upvoted Answer
Find the guided wavelength if the distance between the two conducting ...
The guided wavelength in a waveguide is given by the formula:
λg = λ / √(1 - (λ / 2a)^2)
Given:
Distance between the two conducting plates (a) = 2 cm
To calculate the guided wavelength:
1. Convert the distance between the plates into meters:
a = 2 cm = 0.02 m
2. Substitute the value of 'a' into the formula:
λg = λ / √(1 - (λ / 2(0.02))^2)
3. Simplify the equation:
λg = λ / √(1 - (λ / 0.04)^2)
λg = λ / √(1 - λ^2 / 0.0016)
λg = λ / √((0.0016 - λ^2) / 0.0016)
λg = λ * √(0.0016 / (0.0016 - λ^2))
4. Since we don't have the value of λ, we can assume a value and calculate the guided wavelength. Let's assume λ = 2 cm (0.02 m) for simplicity.
5. Substitute the assumed value into the equation:
λg = 0.02 * √(0.0016 / (0.0016 - (0.02)^2))
λg = 0.02 * √(0.0016 / (0.0016 - 0.0004))
λg = 0.02 * √(0.0016 / 0.0012)
λg = 0.02 * √1.3333
λg = 0.02 * 1.1547
λg = 0.0231 m = 2.31 cm
Conclusion:
The guided wavelength in the waveguide is approximately 2.31 cm. Therefore, option 'A' is the correct answer.
λg = λ / √(1 - (λ / 2a)^2)
Given:
Distance between the two conducting plates (a) = 2 cm
To calculate the guided wavelength:
1. Convert the distance between the plates into meters:
a = 2 cm = 0.02 m
2. Substitute the value of 'a' into the formula:
λg = λ / √(1 - (λ / 2(0.02))^2)
3. Simplify the equation:
λg = λ / √(1 - (λ / 0.04)^2)
λg = λ / √(1 - λ^2 / 0.0016)
λg = λ / √((0.0016 - λ^2) / 0.0016)
λg = λ * √(0.0016 / (0.0016 - λ^2))
4. Since we don't have the value of λ, we can assume a value and calculate the guided wavelength. Let's assume λ = 2 cm (0.02 m) for simplicity.
5. Substitute the assumed value into the equation:
λg = 0.02 * √(0.0016 / (0.0016 - (0.02)^2))
λg = 0.02 * √(0.0016 / (0.0016 - 0.0004))
λg = 0.02 * √(0.0016 / 0.0012)
λg = 0.02 * √1.3333
λg = 0.02 * 1.1547
λg = 0.0231 m = 2.31 cm
Conclusion:
The guided wavelength in the waveguide is approximately 2.31 cm. Therefore, option 'A' is the correct answer.
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Find the guided wavelength if the distance between the two conducting plates in the waveguide is 2 cm.a)4cmb)2cmc)1cmd)0.5cmCorrect answer is option 'A'. Can you explain this answer?
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