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QUESTION: 1

In a waveguide, which of the following condition is true always?

Solution:

Answer: c

Explanation: The phase velocity is always greater than the speed of light in waveguides. This implies the group velocity is small.

QUESTION: 2

The term cos θ is given by 2.5. Find the phase velocity.

Solution:

Answer: c

Explanation: The phase velocity is given by Vp = c cos θ. On substituting for cos θ = 2.5 and the speed of light, we get the phase velocity as 7.5 x 10^{8} m/s.

QUESTION: 3

The cut off wavelength and the guided wavelength are given by 0.5 and 2 units respectively. Find the wavelength of the wave.

Solution:

Answer: a

Explanation: The cut off wavelength and the guided wavelength are related as (1/λ)^{2} = (1/λc)^{2} + (1/λg)^{2}. On substituting for λc = 0.5 and λg = 2, we get λ = 0.48 units.

QUESTION: 4

The cut off wavelength of the rectangular waveguide in dominant mode with dimensions 6 cm x 4 cm is

Solution:

Answer: a

Explanation: The cut off wavelength in the dominant mode is given by λc = 2a/m, where a is the broad wall dimension. On substituting for m = 1 and a = 6cm, we get the cut off wavelength as 12cm.

QUESTION: 5

The product of the phase and the group velocities is given by the

Solution:

Answer: d

Explanation: The product of the phase and the group velocities is given by the square of the speed of the light. Thus Vp x Vg = c^{2} is the relation.

QUESTION: 6

The phase velocity of a wave having a group velocity of 6 x 10^{6} is (in order of 10^{8} m/s)

Solution:

Answer: d

Explanation: We know that the phase and the group velocities are given by Vp x Vg = c^{2}. On substituting for Vg = 6 x 10^{6} and the speed of light, we get Vp = 150 x 10^{8} m/s.

QUESTION: 7

The group velocity of a wave with a phase velocity of 60 x 10^{9} is (in 10^{6} order)

Solution:

Answer: a

Explanation: We know that the phase and the group velocities are given by Vp x Vg = c^{2}. On substituting for Vp = 60 x 10^{9} and the speed of light, we get Vg = 1.5 x 10^{6} m/s.

QUESTION: 8

The phase velocity of a wave having a phase constant of 4 units and a frequency of 2.5 x 10^{9} radian/sec is (in 10^{8} order)

Solution:

Answer: c

Explanation: The phase velocity and the phase constant are related by Vp = ω/βg. On substituting for ω = 2.5 x 10^{9} and β = 4, we get the phase velocity as 6.25 units.

QUESTION: 9

The guided wavelength and the phase constant are related by

Solution:

Answer: a

Explanation: The guided wavelength and the phase constant are related by 2π/βg = λg, where βg is the guided phase constant and λg is the guided wavelength.

QUESTION: 10

The phase velocity refers to a group of waves and the group velocity refers to a single wave. State true/false.

Solution:

Answer: b

Explanation: The phase velocity refers to a single wave and the group velocity refers to a group of waves.

QUESTION: 11

The phase and group velocities does not depend on which of the following?

Solution:

Answer: d

Explanation: The phase and the group velocities are directly related by the frequency, wavelength and the phase constant. It is independent of the attenuation constant.

QUESTION: 12

The distance between two successive points in a waveguide is the

Solution:

Answer: c

Explanation: The distance between two successive points in a waveguide is equal to half of the guided wavelength.

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