A wave of 100 MHz in a medium of relative permittivity 2.25 has a wavelength of
Answer: D
The free space wavelength is three metres and the square root of 2.25 is 1.5, so the wavelength in the medium is two metres. A relative permittivity of 2.25 corresponds to a refractive index of exactly 1.5, which is that of ordinary glass.
Please log in or register to report this question.
A wave reflected at a boundary with a reflection coefficient of 0.5 gives a standing wave ratio of
Answer: A
Correct answer: 3
\[ \mathrm{SWR} = \frac{1+|\Gamma|}{1-|\Gamma|} = \frac{1.5}{0.5} = 3. \] The ratio runs from 1 for a matched boundary to infinity for total reflection, so it is a convenient measure precisely because it turns the small numerical range of \( |\Gamma| \) into something easier to read on an instrument.
Please log in or register to report this question.
A reflection coefficient of 0.5 in amplitude corresponds to a reflected power of
Answer: B
Power is proportional to the square of the field amplitude, so half the amplitude is a quarter of the power. Three quarters of the incident power is therefore transmitted, which is a useful check on any such calculation.
Please log in or register to report this question.
A wave attenuates by 1 neper per metre. After 3 m its amplitude is reduced to
Answer: C
Correct answer: about 5 per cent of its initial value
The amplitude falls as \( e^{-\alpha z} \), so after 3 m at 1 neper per metre it is \[ e^{-3} = 0.0498, \] about 5 per cent. The 37 per cent offered is \( e^{-1} \), the reduction after a single metre - the trap is treating the neper as a fixed fraction rather than as an exponent that accumulates with distance.
Please log in or register to report this question.
The intrinsic impedance of free space is
Answer: D
Its exact value is \( 120\pi \) ohms in the old system of units, and it fixes the ratio of the electric to the magnetic field in any plane wave in vacuum. It has nothing to do with the characteristic impedance of a particular cable.
Please log in or register to report this question.
A plane wave has an electric field amplitude of 10 V/m in free space. Its magnetic field amplitude is about
Answer: A
Dividing by the intrinsic impedance gives \( 10/377 = 2.65 \times 10^{-2} \) A/m. The great disparity in the numerical values is entirely an artefact of the units chosen, the two fields carrying equal energy densities in a plane wave.
Please log in or register to report this question.
True or false: a plane wave can have a component of electric field along its direction of travel.
Answer: B
The divergence condition forces the longitudinal component to be constant along the direction of propagation, and for a wave it must therefore vanish. Guided waves in a hollow waveguide do have longitudinal components, but they are not uniform plane waves.
Please log in or register to report this question.
True or false: the phase velocity can exceed the speed of light in vacuum.
Answer: C
The phase velocity is the speed of a point of constant phase and carries no information, so no principle forbids it exceeding c, and in a waveguide it does. The group velocity, which carries the energy, remains below c.
Please log in or register to report this question.
True or false: an unpolarised wave has no electric field.
Answer: D
Unpolarised light is a rapid and random superposition of all polarisations, so the field is present at every instant but its direction changes unpredictably. A single monochromatic plane wave is always polarised in some sense.
Please log in or register to report this question.
True or false: the reflection coefficient at a boundary can exceed unity in magnitude.
Answer: A
Correct answer: False for a passive boundary, the reflected power then exceeding the incident
A passive boundary cannot return more power than arrives, and since the reflected power goes as \( |\Gamma|^2 \), a magnitude above one would violate conservation of energy. The coefficient can be negative, as at a perfect conductor where it is exactly \( -1 \), and it can be complex for a lossy second medium - but its magnitude never exceeds unity.
Please log in or register to report this question.
