Two galaxies with an angular separation at the observer of \(5.0 \times {10^{ - 4}}\) radians are observed with a radio telescope. Both galaxies emit radio waves of wavelength \(2.5 \times {10^{ - 2}}{\text{ m}}\).

The images of the galaxies are just resolved by the telescope. The diameter of the circular collecting dish of the telescope is

A.     61 m.

B.     50 m.

C.     30 m.

D.     25 m.

A diffraction grating is used to observe light of wavelength 400 nm. The light illuminates 100 slits of the grating. What is the minimum wavelength difference that can be resolved when the second order of diffraction is viewed? 

A. 1 nm 

B. 2 nm 

C. 4 nm 

D. 8 nm

A mass oscillates with simple harmonic motion (SHM) of amplitude x_o. Its total energy is 16 J. 

What is the kinetic energy of the mass when its displacement is \(\frac{{{x_0}}}{2}\)?

A. 4 J

B. 8 J

C. 12 J

D. 16 J

Monochromatic light is incident on two identical slits to produce an interference pattern on a screen. One slit is then covered so that no light emerges from it. What is the change to the pattern observed on the screen?

A. Fewer maxima will be observed.

B. The intensity of the central maximum will increase.

C. The outer maxima will become narrower.

D. The width of the central maximum will decrease.

Two lines X and Y in the emission spectrum of hydrogen gas are measured by an observer stationary with respect to the gas sample.

The emission spectrum is then measured by an observer moving away from the gas sample.

What are the correct shifts X* and Y* for spectral lines X and Y?

Light of wavelength λ is incident normally on a diffraction grating that has a slit separation of \(\frac{{7\lambda }}{2}\). What is the greatest number of maxima that can be observed using this arrangement? 

A. 4 
B. 6 
C. 7 
D. 9

Which of the following wave phenomena is associated with blood flow measurements?

A.     Polarization

B.     Diffraction

C.     Refraction

D.     Doppler effect

Monochromatic light of wavelength λ in air is incident normally on a thin film of refractive index n. The film is surrounded by air. The intensity of the reflected light is a minimum. What is a possible thickness of the film?

A.     \(\frac{\lambda }{{4n}}\)

B.     \(\frac{{3\lambda }}{{4n}}\)

C.     \(\frac{\lambda }{n}\)

D.     \(\frac{{5\lambda }}{{4n}}\)

Monochromatic light is incident on 4 rectangular, parallel slits. The first principal maximum is observed at an angle θ to the direction of the incident light. The number of slits is increased to 8 each having the same width and spacing as the first 4.

Three statements about the first principal maximum with 8 slits are

     I.     the angle at which it is observed is greater than θ

     II.     its intensity increases

     III.     its width decreases.

Which statements are correct?

A.     I and II only

B.     I and III only

C.     II and III only

D.     I, II and III 

A simple pendulum bob oscillates as shown.

At which position is the resultant force on the pendulum bob zero?

A.     At position A

B.     At position B

C.     At position C

D.     Resultant force is never zero during the oscillation

A pendulum oscillating near the surface of the Earth swings with a time period T. What is the time period of the same pendulum near the surface of the planet Mercury where the gravitational field strength is 0.4g?

A.  0.4T

B.  0.6T

C.  1.6T

D.  2.5T

A spring loaded with mass m oscillates with simple harmonic motion. The amplitude of the motion is A and the spring has total energy E. What is the total energy of the spring when the mass is increased to 3m and the amplitude is increased to 2A?

A. 2E

B. 4E

C. 12E

D. 18E

A beam of coherent light is incident on a single slit of width \(b\). After passing through the slit, the light is incident on a screen at a distance \(D\) from the slit.

Which of the following changes, carried out separately, in respect of \(b\) and \(D\) will result in an increase in width of the first diffraction maximum formed on the screen?

A parallel beam of coherent light of wavelength λ is incident on a rectangular slit of width d. After passing through the slit the light is incident on a screen a distance D from the slit where D is much greater than d. What is the width of the central maximum of the diffraction pattern as measured on the screen?

A. \(\frac{{2D\lambda }}{d}\)

B. \(\frac{{2d}}{{D\lambda }}\)

C. \(\frac{{D\lambda }}{d}\)

D. \(\frac{d}{{D\lambda }}\)

A single-slit diffraction experiment is performed using light of different colours. The width of the central peak in the diffraction pattern is measured for each colour. What is the order of the colours that corresponds to increasing widths of the central peak?

A. red, green, blue

B. red, blue, green

C. blue, green, red

D. green, blue, red

A beam of monochromatic light is incident on a single slit and a diffraction pattern forms on the screen.

What change will increase θ_s?

A.     Increase the width of the slit

B.     Decrease the width of the slit

C.     Increase the distance between the slit and the screen

D.     Decrease the distance between the slit and the screen

Green light is emitted by two point sources. The light passes through a narrow slit and is received by an observer. The images of the two sources just fail to be resolved. Which change allows for the images to be resolved?

A. Replacing the narrow slit with a circular aperture of same size.

B. Moving the two sources further from the aperture.

C. Using red light.

D. Using violet light.

A mass at the end of a vertical spring and a simple pendulum perform oscillations on Earth that are simple harmonic with time period T. Both the pendulum and the mass-spring system are taken to the Moon. The acceleration of free fall on the Moon is smaller than that on Earth. What is correct about the time periods of the pendulum and the mass-spring system on the Moon?

A train travelling in a straight line emits a sound of constant frequency f. An observer at rest very close to the path of the train detects a sound of continuously decreasing frequency. The train is

A. approaching the observer at constant speed.

B. approaching the observer at increasing speed.

C. moving away from the observer at constant speed.

D. moving away from the observer at increasing speed.

A particle is oscillating with simple harmonic motion (shm) of amplitude x₀ and maximum kinetic energy E_k. What is the potential energy of the system when the particle is a distance 0.20x₀ from its maximum displacement? 

A. 0.20E_k 

B. 0.36E_k 

C. 0.64E_k 

D. 0.80E_k

A transparent liquid forms a parallel-sided thin film in air. The diagram shows a ray I incident on the upper air–film boundary at normal incidence (the rays are shown at an angle to the normal for clarity).

Reflections from the top and bottom surfaces of the film result in three rays J, K and L. Which of the rays has undergone a phase change of \(\pi \) rad?

A. J only

B. J and L only

C. J and K only

D. J, K and L

A beam of monochromatic light is incident on a diffraction grating of N lines per unit length. The angle between the first orders is θ₁.

What is the wavelength of the light?

A.     \(\frac{{\sin {\theta _1}}}{N}\)

B.     N sin θ₁

C.     N sin\(\left( {\frac{{{\theta _1}}}{2}} \right)\)

D.     \(\frac{{\sin \left( {\frac{{{\theta _1}}}{2}} \right)}}{N}\)

A source of sound approaches a stationary observer. The speed of the emitted sound and its wavelength, measured at the source, are \(\nu \) and \(\lambda \) respectively. Which of the following is the wave speed and the wavelength, as measured by the stationary observer?

A stationary source of sound emits sound of frequency f. A moving observer measures the sound as having the frequency f ′. The observer is moving directly away from the source at a speed that is 30% of the speed of sound in air.

Which of the following gives the correct value for \(\frac{{f'}}{f}\)?

A. \(\frac{7}{{10}}\)

B. \(\frac{10}{{13}}\)

C. \(\frac{13}{{10}}\)

D. \(\frac{10}{{7}}\)

An object to be viewed by a microscope is irradiated with blue light. The reason for using blue light rather than light of a longer wavelength is to increase

A. diffraction.
B. interference.
C. resolution.
D. magnification.

The images of two sources are just resolved. Which of the following is a correct statement of the Rayleigh criterion for this situation?

A.     The central maximum of the diffraction pattern of one source must coincide with the central maximum of the diffraction pattern of the other source.

B.     Light from the sources must pass through a circular aperture.

C.     Light from the sources must be coherent.

D.     The first minimum of the diffraction pattern of one source must coincide with the central maximum of the diffraction pattern of the other source.

Light of wavelength λ is emitted by two point sources. The light passes through a circular aperture of diameter b and is received by an observer. The angular separation of the sources from the observer’s position is θ. The sources are not resolved by the observer. Which of the following mathematical relationships applies?

A. \(\theta  < 1.22\frac{\lambda }{b}\)

B. \(\theta  > 1.22\frac{\lambda }{b}\)

C. \(\theta  = 1.22\frac{\lambda }{b}\)

D. \(\theta  = \frac{\lambda }{b}\)

A car horn emits sound of frequency ƒ. While the horn is sounding, the car moves in a straight line towards a stationary observer. The speed of the car is 0.10v where v is the speed of sound. What is the frequency of the sound of the horn heard by the observer?

1. \(\frac{f}{{0.90}}\)
2. 1.1 ƒ
3. \(\frac{f}{{1.1}}\)
4. 0.90 ƒ

A train is approaching an observer with constant speed

                                                         \[\frac{c}{{34}}\]

where c is the speed of sound in still air. The train emits sound of wavelength λ. What is the observed speed of the sound and observed wavelength as the train approaches?

A source emits sound of wavelength \({\lambda _0}\) and wave speed \({v_0}\). A stationary observer hears the sound as the source moves away. What are the wavelength of the sound and the wave speed of the sound as measured by the stationary observer?

A siren on an ambulance emits sound of frequency f. The speed of sound in still air is v. What is the frequency of the sound observed when the ambulance travels at speed \(\frac{v}{{10}}\) towards a stationary observer?

A. \(\frac{f}{{10}}\)

B. f

C. \(\frac{{11}}{{10}}f\)

D. \(\frac{{10}}{{9}}f\)

During a journey an observer travels at constant speed towards, and then goes beyond, a stationary emitter of sound.

The frequency of the sound as measured at the emitter is \(f\). The frequency according to the observer

A.     is always greater than \(f\).

B.     is always equal to \(f\).

C.     is always less than \(f\).

D.     varies during the journey.

A body moves with simple harmonic motion (SHM) with period T and total energy E_T. What is the total energy when the period of the motion is changed to 5T and the amplitude of the motion remains constant?

A. 0.04 E_T

B. 0.2 E_T

C. 5 E_T

D. 25 E_T

A sample of hydrogen on Earth emits a spectral line that is measured by an Earth observer to have wavelength 500 nm. The same spectral line is emitted by a galactic source that is moving away from Earth at speed of 0.1c. What is the wavelength of the galactic spectral line that will be measured by the Earth observer?

A. 50 nm
B. 450 nm
C. 550 nm
D. 5000 nm

Two coloured point sources are observed through an optical telescope. Which of the following colours for the sources would best allow their images to be resolved?

A. Blue
B. Green
C. Red
D. Yellow

Two point sources of light have an angular separation of θ, as measured by a distant observer. The light passes through a circular aperture of radius r just before reaching the observer. Which of the following conditions must be true for the two sources to be resolved?

A. \(\theta  < 0.61\frac{\lambda }{r}\)

B. \(\theta  < 1.22\frac{\lambda }{r}\)

C. \(\theta  \ge 0.61\frac{\lambda }{r}\)

D. \(\theta  \ge 1.22\frac{\lambda }{r}\)

A radio telescope has a circular collecting dish of diameter 5.0 m. It is used to observe two distant galaxies that are both emitting electromagnetic radiation of wavelength 20 cm. The images of the galaxies are just resolved by the telescope. What is the angle subtended by the galaxies at the telescope?

A.     0.05 rad

B.     0.3 rad

C.     5 rad

D.     30 rad

A source of sound moves away from an observer. The observed frequency of the sound differs from the frequency emitted by the source because the

A. observed wavelength of the sound is less than the emitted wavelength.
B. observed wavelength of the sound is greater than the emitted wavelength.
C. speed of sound relative to the observer has decreased.
D. speed of sound relative to the observer has increased.

Which of the following would be diffracted the most when incident on a slit of width 1 cm?

A. microwaves

B. red light

C. ultraviolet

D. X-rays

Blue light is incident on two narrow slits. Constructive interference takes place along the lines labelled 1 to 5.

The blue light is now replaced by red light. What additional change is needed so that the lines of constructive interference remain in the same angular positions?

A. Make the slits wider

B. Make the slits narrower

C. Move the slits closer together

D. Move the slits further apart

A stationary sound source emits waves of wavelength \(\lambda \) and speed v. The source now moves away from a stationary observer. What are the wavelength and speed of the sound as measured by the observer?

A parallel beam of monochromatic light of wavelength \(\lambda \) passes through a slit of width \(b\). After passing through the slit the light is incident on a distant screen. The angular width of the central maximum is

A.     \({\text{2}}\frac{\lambda }{b}\) radians.

B.     \(\frac{\lambda }{b}\) radians.

C.     \(2\frac{\lambda }{b}\) degrees.

D.     \(\frac{\lambda }{b}\) degrees.

For fringes to be observed in a double-slit interference experiment, the slits must emit waves that are coherent.

What conditions are required for the frequency of the waves and for the phase difference between the waves so that the waves are coherent?

A train moving at speed u relative to the ground, sounds a whistle of constant frequency f as it moves towards a vertical cliff face.

The sound from the whistle reaches the cliff face and is reflected back to the train. The speed of sound in stationary air is c.

What whistle frequency is observed on the train after the reflection?

A.  \(\frac{{(c + u)}}{{(c - u)}}f\)

B.  (c + u)f

C.  (c – u)f

D.  \(\frac{{(c - u)}}{{(c + u)}}f\)

Two points illuminated by monochromatic light are separated by a small distance. The light from the two sources passes through a small circular aperture and is detected on a screen far away.

Two points illuminated by monochromatic light are separated by a small distance. The light from the two sources passes through a small circular aperture and is detected on a screen far away.

An object emitting a sound of frequency 100 Hz orbits in a horizontal circle at a rate of two revolutions per second.

An observer standing a short distance away from the object is able to hear the sound. Which of the following describes the sound the observer is able to hear?

A. A sound of constant frequency but varying in amplitude

B. A sound of constantly varying frequency

C. A sound with a frequency of 50 Hz

D. A sound with a frequency of 200 Hz

The graph below shows the variation of the intensity of light with angle for the diffraction pattern produced when light is diffracted by a slit.

According to the Rayleigh criterion, when the diffraction patterns of two slits are just resolved

A. the first maximum of one diffraction pattern coincides with the central maximum of the other diffraction pattern.

B. the central maximum of one diffraction pattern coincides with the central maximum of the other diffraction pattern.

C. the first minimum of one diffraction pattern coincides with the central maximum of the other diffraction pattern.

D. the first minimum of one diffraction pattern coincides with the first minimum of the other diffraction pattern.

An optical instrument is used to observe an object illuminated with monochromatic light. Which of the following changes to the frequency of the light and to the aperture diameter of the optical instrument will increase the resolution of the image of the object formed by the instrument?

The diagram shows a train travelling in a straight line at constant speed v, as it approaches the platform of a station.

The whistle of the engine is emitting a sound of constant frequency. Which of the following is not true for the sound of the whistle heard by an observer on the platform?

A. A sudden change in frequency of the sound as the train passes the observer.
B. A sound of constant frequency as the train approaches the observer.
C. A sound of increasing frequency as the train approaches the observer and of decreasing frequency after the train has passed the observer.
D. A sound of constant frequency after the train has passed the observer.

Monochromatic light is incident on a double slit. Both slits have a finite width. The light then forms an interference pattern on a screen some distance away. Which graph shows the variation of intensity with distance from the centre of the pattern?

A coherent beam of light of wavelength λ is incident on a double slit. The width of the slits is small compared to their separation. An interference pattern is observed on a distant screen. O is the mid point of the screen.

There is a bright fringe at O and a bright fringe at P. Between O and P there are three dark fringes.

Which of the following is the path difference between the light from the two slits arriving at P?

A. 1.5 λ
B. 2 λ
C. 3 λ
D. 4 λ

Light of wavelength λ₀ is emitted from a nearby galaxy. The light is received on Earth and the wavelength is measured to be λ where λ<λ₀. Which of the following correctly describes the speed and direction of motion of the galaxy?

An object undergoes simple harmonic motion. Which graph shows the relationship between the acceleration a and the displacement x from the equilibrium position?

A fire engine with its siren sounding approaches and passes a stationary observer. The frequency of the sound emitted by the siren is \({f_s}\). The frequency of the sound measured by the observer is \({f_o}\). Which of the following describes the relationship between  \({f_o}\) and \({f_s}\)?

Radiation is incident on a single rectangular slit. The diffracted beam that emerges from the slit is incident on a screen. The slit width is then doubled and the wavelength of the radiation is also doubled. The intensity of the radiation remains the same.

Which of the following correctly describes the angular width of the central maximum of the diffracted beam and the total number of photons incident every second on the screen?

The intensity distribution of monochromatic light passing through a narrow slit and then incident on a screen is shown below.

When the slit width is reduced which diagram shows the new intensity distribution? Diagrams are drawn to the same scale as the original.

A parallel beam of monochromatic light of wavelength λ passes through a slit of width b and forms a diffraction pattern on a screen far from the slit. The angle at which the first diffraction minimum is formed is θ.

Which of the following changes in λ and b, carried out separately, will increase the value of θ?

An ambulance emits a sound of frequency f as it travels along a straight road between stationary observers A and B.

Which of the following shows how the frequency of the sound heard by each observer compares with f?

A point source of sound is moving to the right at constant speed. The source emits sound waves of constant frequency. The speed of the source is less than the speed of sound. Which diagram correctly shows the wavefronts of the sound?