P.3.3.1.3 Superposition; stationary waves

A uniform wire, fixed at both ends, is plucked in the middle so that it vibrates at the first harmonic as shown.

What is the phase difference between the oscillations of the particles at P and Q?

• zero

• π/4 rad

• π/2 rad

• 3π/4 rad

Which of the following statements about the behaviour of waves is incorrect?

• All waves can be diffracted.

• All waves can be made to undergo superposition.

• All waves can be refracted

• All waves can be polarised.

Two radio transmitters emit waves at a frequency of 1.4 MHz. A stationary wave is set up between the two transmitters due to the superposition of the radio waves.

What is the minimum distance between two nodes in the stationary wave?

• 107 m

• 214 m

• 428 m

• 857 m

Which of the following is correct for a stationary wave?

• Between two nodes the amplitude of the wave is constant.

• The two waves producing the stationary wave must always be 180° out of phase.

• The separation of the nodes for the second harmonic is double the separation of nodes for the first harmonic

• Between two nodes all parts of the wave vibrate in phase.

The frequency of the first harmonic of a standing wave on a wire is f. The length of the wire and tension in the wire are both doubled.

What is the frequency of the first harmonic as a result?

• $\frac{f}{\sqrt{2}}$

• $f$

• $\sqrt{2}f$

• $2f$

A microwave transmitter is used to direct microwaves of wavelength 30 mm along a line XY. A metal plate is positioned at right angles to XY with its mid-point on the line, as shown.

When a detector is moved gradually along XY, its reading alternates between maxima and minima. Which one of the following statements is not correct?

• The distance between two minima could be 15 mm.

• The distance between two maxima could be 30 mm.

• The distance between a minimum and a maximum could be 30 mm.

• The distance between a minimum and a maximum could be 37.5 mm.

A stationary wave is formed by two identical waves of frequency 300 Hz travelling in opposite directions along the same line. If the distance between adjacent nodes is 0.60 m, what is the speed of each wave?

• 180 m s⁻¹

• 250 m s⁻¹

• 360 m s⁻¹

• 500 m s⁻¹

Which line, A to D, in the table gives a correct difference between a progressive wave and a stationary wave?

• A

• B

• C

• D

Stationary waves are set up on a length of rope fixed at both ends. Which one of the following statements is true?

• Between adjacent nodes, particles of the rope vibrate in phase with each other.

• The mid point of the rope is always stationary.

• Nodes need not necessarily be present at each end of the rope.

• Particles of the rope at adjacent antinodes always move in the same direction.

A uniform wire fixed at both ends is vibrating in its fundamental mode. Which one of the following statements is not correct for all the vibrating particles?

• They vibrate in phase.

• They vibrate with the same amplitude.

• They vibrate with the same frequency.

• They vibrate at right angles to the wire.