Waves

• A stationary or standing wave is produced when a progressive wave is reflected between two fixed points, so that two waves of the same frequency and amplitude, travelling in opposite directions, meet and suppose/interfere, creating regions of nodes and antinodes.
• 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

  
• 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?
• 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 a minimum and a maximum could be 30 mm.
• The fundamental frequency f is the lowest frequency heard when a stretched string is vibrating. The string is now lightly touched one third of the way along its length. What is the lowest frequency heard?

  3f
• A pipe, open at both ends, has a first harmonic of 30Hz. The frequency of the second harmonic is:

  60Hz
• Two loudspeakers emit sound waves. Which line in the table gives the correct frequency condition and the correct phase condition for the waves from the loudspeakers to be coherent?

  Same Frequency and constant phase difference
• In the diagram, P is the source of a wave of frequency 50 Hz.

  The wave travels to R by two routes, P → Q → R and P → R. The speed of the wave is 30 m s−1 What is the path difference between the two waves at R in terms of the wavelength λ of the waves?

  13.3λ

  
• Monochromatic light of wavelength 600 nm is used to illuminate a pair of slits 0.50 mm apart. The fringes are observed at a distance of 1.50 m from the slits. What is the separation of the fringes?

  1.8 mm
• Light from a point source passes through a single slit and is then incident on a double-slit arrangement. An interference pattern is observed on the screen. What will increase the fringe spacing?

  decreasing the separation of the double slits
• White light passes through a single narrow slit and illuminates a screen. What is observed on the screen?

  a white central maximum surrounded by coloured fringes
• The diagram shows a stationary wave on a string at one instant in time.

  A

  
• Microwaves from a transmitter are incident on a gap between two metal plates. The microwaves that pass through the gap are detected by a receiver. The receiver is placed at O. What change causes the received signal to decrease and then increase?

  move the receiver towards X

  
• The diagram shows two charges, +4 µC and –16 µC, 120 mm apart. What is the distance from the +4 µC charge to the point between the two charges, where the resultant electric potential is zero?

  24mm

  
• 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?

  360ms^-1
• A diffraction grating has 500 lines per mm. When monochromatic light is incident normally on the grating the third-order spectral line is formed at an angle of 60° from the normal to the grating. What is the wavelength of the monochromatic light?

  580nm
• Which of the following statements is true?

  A

  
• An object of mass m undergoes undamped simple harmonic motion of amplitude A and frequency f. The phase difference between the variation of displacement with time and the variation of acceleration with time for the body is π rad.
• A graph of acceleration against displacement is a straight line through the origin.
• The total energy of the object is $2π^2mf^2A^2.$
• Two transmitters emit microwaves. In order to detect and observe a stable interference pattern the two wave sources must be coherent. The two sources should have the same frequency and a constant phase difference,
• Light passes through a diffraction grating and illuminates a screen. Violet light is diffracted less than red light for a given spectral order.
• Monochromatic light is incident on a single slit. Light from the single slit subsequently illuminates two narrow slits, A and B.

  An interference pattern of bright and dark fringes is observed on a screen placed some distance D away from the two slits A and B.

  When only the distance D is increased, the separation of the fringes increases.
• If a diffraction grating, used to observe spectra, is replaced by one having twice as many rulings per millimetre, which of the following statements are correct?

  1. The angle of diffraction is doubled for every spectral line.
  2. The gaps between the first and second order spectra are narrowed.
  3. The spectra all appear wider than before.
• A guitar string is vibrating in the third harmonic.

  All particles within a loop reach their maximum amplitude simultaneously.

  Particles in adjacent loops vibrate in antiphase.

  All particles vibrate with the same frequency
• A monochromatic light source is incident on a single slit. Light from the single slit subsequently illuminates two narrow slits, X and Y.

  An interference pattern of bright and dark fringes is observed on a screen placed some distance D away from the two slits X and Y.

  Using monochromatic light of higher frequency decreases the separation of the fringes, if all other factors remain unaltered.
• A monochromatic light source is incident on a single slit. Light from the single slit subsequently illuminates two narrow slits, X and Y.

  An interference pattern of bright and dark fringes is observed on a screen placed some distance D away from the two slits X and Y.

  When only the distance D is increased, the separation of the fringes increases.
• A monochromatic light source is incident on a single slit. Light from the single slit subsequently illuminates two narrow slits, X and Y.

  An interference pattern of bright and dark fringes is observed on a screen placed some distance D away from the two slits X and Y.

  The fringe spacing is independent of the width of the single slit.
• When a monochromatic light source is incident on two slits of the same width an interference pattern is produced. One slit is then covered with opaque black paper. What is the effect of covering one slit on the resulting interference pattern?

  Fewer maxima are observed
• for a stationary wave Between two nodes all parts of the wave vibrate in phase.
• In a standing wave, the wavelength is equal to twice the length of the medium that is oscillating.
• For a standing wave between two anti-nodes all parts of the wave vibrate out of phase.
• In a standing wave, the number of half waves between any two successive nodes or anti-nodes is always an integer.
• For a standing wave between two fixed points, the amplitude at any point is directly proportional to the number of half-wavelengths contained within the region bounded by those two points.
• 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?

  $f/sqrt(2)$
• Coherent monochromatic light of wavelength λ emerges from the slits X and Y to form dark fringes at P, Q, R and S in a double slit apparatus. Which one of the following statements is true?

  When the distance D is increased, the separation of the fringes increases.
• If the wavelength of light is decreased, then the angular spread of the diffracted rays would increase.
• stationary waves - Particles immediately on either side of a node are moving in opposite directions.
• In a double slit system used to produce interference fringes, the separation of the slits is s and the width of each slit is x. L is a source of monochromatic light. Which one of the following changes would decrease the separation of the fringes seen on the screen?

  moving the screen closer to the double slits
• In a Young’s double slit interference experiment, monochromatic light placed behind a single slit illuminates two narrow slits and the interference pattern is observed on a screen placed some distance away from the slits. Which one of the following decreases the separation of the fringes?

  using monochromatic light of higher frequency