22P2Q05

5ai)

1. A standing wave has nodes where the amplitude of oscillation is zero, and antinode where the amplitude is maximum.

2. The oscillations are in-phase in the same loop, but completely out of phase in adjacent loops.

5b)

The microwave undergoes reflection when it hits the metal plate.

The incident wave and reflected wave superpose to result in a standing wave.

5ci)

A minimum is formed when the incident and reflected wave superpose in antiphase.

However, the incident and reflected wave have different amplitudes because as a wave propagates, its intensity decreases following to the inverse-square law. (\displaystyle I\propto \frac{1}{{{r}^{2}}})

The resultant minimum therefore does not have zero amplitude, and thus intensity is not zero.

COMMENT: In addition to wave amplitude continuously decreasing with distance, the amplitude may also suffer an abrupt drop at the reflection due to absorption of energy by the metal plate.

5cii)

\displaystyle \lambda &=5.2\text{ cm}

COMMENT: The distance between two consecutive nodes (or antinodes) is half a wavelength.

5ciii)

\displaystyle \begin{aligned}   v&=f\lambda  \\  3.0\times {{10}^{8}}&=f(0.052) \\  f&=5.77\times {{10}^{9}}\text{ Hz} \end{aligned}

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