DP Physics Questionbank

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

Airports use radar to track the position of aircraft. The waves are reflected from the aircraft and detected by a large circular receiver. The receiver must be able to resolve the radar images of two aircraft flying close to each other.

The following data are available.

Calculate the minimum distance between the two aircraft when their images can just be resolved.

Police use radar to detect speeding cars. A police officer stands at the side of the road and points a radar device at an approaching car. The device emits microwaves which reflect off the car and return to the device. A change in frequency between the emitted and received microwaves is measured at the radar device.

The frequency change Δf is given by

$$\mathrm{\Delta }f=\frac{2fv}{c}$$

where f is the transmitter frequency, v is the speed of the car and c is the wave speed.

The following data are available.

(i) Explain the reason for the frequency change.

(ii) Suggest why there is a factor of 2 in the frequency-change equation.

(iii) Determine whether the speed of the car is below the maximum speed allowed.

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 second identical spring is placed in parallel and the experiment in (b) is repeated. Suggest how this change affects the fractional uncertainty in the mass of the block.

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.  $\frac{(c-u)}{(c+u)}f$

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

Calculate the mass of the wooden block.

In carrying out the experiment the student displaced the block horizontally by 4.8 cm from the equilibrium position. Determine the total energy in the oscillation of the wooden block.

Describe the conditions required for an object to perform simple harmonic motion (SHM).

Sketch a graph to show the variation with time of the generator output power. Label the time axis with a suitable scale.

Determine the width of one of the slits.

A wave of amplitude 4.3 m and wavelength 35 m, moves with a speed of 3.4 m s^–1. Calculate the maximum vertical speed of the buoy.

Light is incident on a diffraction grating. The wavelengths of two spectral lines of the light differ by $0.59 \mathrm{nm}$ and have a mean wavelength of $590 \mathrm{nm}$. The spectral lines are just resolved in the fourth order of the grating. What is the minimum number of grating lines that were illuminated?

A.  $25$

B.  $250$

C.  $1000$

D.  $4000$

A simple pendulum and a mass–spring system oscillate with the same time period. The mass of the pendulum bob and the mass on the spring are initially identical. The masses are halved.

What is $\frac{\mathrm{time} \mathrm{period} \mathrm{of} \mathrm{pendulum}}{\mathrm{time} \mathrm{period} \mathrm{of} \mathrm{mass}–\mathrm{spring} \mathrm{system}}$ when the masses have been changed?

A.  $\frac{\sqrt{2}}{2}$

B.  $1$

C.  $\sqrt{2}$

D.  $2$

Calculate $v$.

The mass of the cylinder is $118 \mathrm{kg}$ and the cross-sectional area of the cylinder is $2.29\times {10}^{-1} {\mathrm{m}}^2$. The density of water is $1.03\times {10}^3 \mathrm{kg} {\mathrm{m}}^{-3}$. Show that the angular frequency of oscillation of the cylinder is about $4.4 \mathrm{rad} {\mathrm{s}}^{-1}$.

Draw, on the axes, the graph to show how the kinetic energy of the cylinder varies with time during one period of oscillation $T$.

Determine the maximum kinetic energy $E_{\mathrm{kmax}}$ of the cylinder.

Monochromatic light of wavelength $\lambda$ passes through a single-slit of width $b$ and produces a diffraction pattern on a screen. Which combination of changes to $b$ and $\lambda$ will cause the greatest decrease in the width of the central maximum?

State and explain the differences between the pattern on the screen due to the grating and the pattern due to the double slit.

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

Calculate the separation of the two slits.

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?

Explain why zero intensity is observed at position A.

Estimate the value of k in the following expression.

T = $2\pi \sqrt{\frac{m}{k}}$

Give an appropriate unit for your answer. Ignore the mass of the cable and any oscillation of satellite X.

The distance from the centre of the pattern to A is 4.1 x 10^–2 m. The distance from the screen to the slits is 7.0 m.

Calculate the width of each slit.

The yellow light is made from two very similar wavelengths that produce two lines in the spectrum of sodium. The wavelengths are 588.995 nm and 589.592 nm. These two lines can just be resolved in the second-order spectrum of this diffraction grating. Determine the beam width of the light incident on the diffraction grating.

Explain the condition for w that eliminates reflection for a particular light wavelength in air ${\lambda }_{\text{air}}$.

The painting contains a pattern of red dots with a spacing of 3 mm. Assume the wavelength of red light is 700 nm. The average diameter of the pupil of a human eye is 4 mm. Calculate the maximum possible distance at which these red dots are distinguished.

State the phase change when a ray is reflected at B.

Calculate, in m s⁻¹, the maximum velocity of vibration of point P when it is vibrating with a frequency of 195 Hz.

Estimate the displacement needed to double the energy of the string.

The separation of adjacent slits is d. Show that for the second-order diffraction maximum $2\lambda =d\sin \theta$.

Monochromatic light of wavelength 633 nm is normally incident on a diffraction grating. The diffraction maxima incident on a screen are detected and their angle θ to the central beam is determined. The graph shows the variation of sinθ with the order n of the maximum. The central order corresponds to n = 0.

Determine a mean value for the number of slits per millimetre of the grating.

The diagram shows the diffraction pattern for light passing through a single slit.

What is

                                      $\frac{\text{wavelength of light}}{\text{width of slit}}$

A. 0.01

B. 0.02

C. 1

D. 2

A mass–spring system oscillates vertically with a period of $T$ at the surface of the Earth. The gravitational field strength at the surface of Mars is $0.3 \text{g}$. What is the period of the same mass–spring system on the surface of Mars?

A.  $0.9T$

B.  $0.3T$

C.  $T$

D.  $3T$

A train is moving in a straight line away from a stationary observer when the train horn emits a sound of frequency $f_0$. The speed of the train is $0.10v$ where $v$ is the speed of sound. What is the frequency of the horn as heard by the observer?

A.  $\frac{0.9}{1}{f}_0$

B.  $\frac{1}{1.1}{f}_0$

C.  $\frac{1.1}{1}{f}_0$

D.  $\frac{1}{0.9}{f}_0$

Calculate, in terms of g, the maximum acceleration of P.

The wavelength of the light in the beam when emitted by the galaxy was 621.4 nm.

Explain, without further calculation, what can be deduced about the relative motion of the galaxy and the Earth.

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.     $\frac{5\lambda }{4n}$

Calculate the speed of the block as it passes the equilibrium position. 

Calculate the angular separation between the central peak and the missing peak in the double-slit interference intensity pattern. State your answer to an appropriate number of significant figures.

Calculate the time taken for the block to return to the equilibrium position for the first time. 

Deduce, in mm, the width of one slit.

determine the initial energy.

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 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?

The slit separation is increased. Outline one change observed on the screen.

Show that the period of oscillation of the ball is about 6 s.

The amplitude of oscillation is 0.12 m. On the axes, draw a graph to show the variation with time t of the velocity v of the ball during one period.

Monochromatic light from two identical lamps arrives on a screen.

The intensity of light on the screen from each lamp separately is I₀.

On the axes, sketch a graph to show the variation with distance x on the screen of the intensity I of light on the screen.

Monochromatic light from a single source is incident on two thin, parallel slits.

The following data are available.

The intensity I of light at the screen from each slit separately is I₀. Sketch, on the axes, a graph to show the variation with distance x on the screen of the intensity of light on the screen for this arrangement.

Monochromatic light of wavelength $\lambda$ in air is incident normally on a thin liquid film of refractive index $n$ that is suspended in air. The rays are shown at an angle to the normal for clarity.

What is the minimum thickness of the film so that the reflected light undergoes constructive interference?

A.  $\frac{\lambda }{4n}$

B.  $\frac{\lambda }{3n}$

C.  $\frac{\lambda }{2n}$

D.  $\frac{\lambda }{n}$

Calculate the period of oscillations of q.

A plate performs simple harmonic oscillations with a frequency of 39 Hz and an amplitude of 8.0 cm.

Show that the maximum speed of the oscillating plate is about 20 m s⁻¹.

Sound of frequency 2400 Hz is emitted from a stationary source towards the oscillating plate in (b). The speed of sound is 340 m s⁻¹.

Determine the maximum frequency of the sound that is received back at the source after reflection at the plate.

A beam of monochromatic light is incident normally on a diffraction grating. The grating spacing is d. The angles between the different orders are shown on the diagram.

What is the expression for the wavelength of light used?

A.   $\frac{d\text{sin}\alpha }{2}$

B.   $\frac{d\text{sin}\beta }{2}$

C.   d sin α

D.   d sin β

The light illuminates a width of 3.5 mm of the grating. The deuterium and hydrogen red lines can just be resolved in the second-order spectrum of the diffraction grating. Show that the grating spacing of the diffraction grating is about 2 × 10^–6m.

An ambulance siren emits a sound of frequency 1200 Hz. The speed of sound in air is 330 m s^–1. The ambulance moves towards a stationary observer at a constant speed of 40 m s^–1. What is the frequency heard by the observer?

A.   $\frac{1200\times 330}{370}$Hz

B.   $\frac{1200\times 290}{330}$Hz

C.   $\frac{1200\times 370}{330}$Hz

D.   $\frac{1200\times 330}{290}$Hz

An object undergoing simple harmonic motion (SHM) has a period T and total energy E. The amplitude of oscillations is halved. What are the new period and total energy of the system?

Light of wavelength $\lambda$ is diffracted after passing through a very narrow single slit of width $x$. The intensity of the central maximum of the diffracted light is $I_0$. The slit width is doubled.

What is the intensity of central maximum and the angular position of the first minimum?

An observer with an eye of pupil diameter $d$ views the headlights of a car that emit light of wavelength $\lambda$. The distance between the headlights is $L$.

What is the greatest distance between the observer and the car at which the images of the headlights will be resolved by the observer’s eye?

A.  $\frac{1.22\lambda }{Ld}$

B.  $\frac{1.22\lambda L}{d}$

C.  $\frac{Ld}{1.22\lambda }$

D.  $\frac{d}{1.22\lambda L}$

Outline two reasons why both models predict that the motion is simple harmonic when $a$ is small.

The graph shows for model A the variation with $x$ of elastic potential energy E_p stored in the spring.

Describe the graph for model B.

Deduce whether the motion of Z is simple harmonic.

Loudspeaker A is switched off. Loudspeaker B moves away from M at a speed of 1.5 m s⁻¹ while emitting a frequency of 3.0 kHz.

Determine the difference between the frequency detected at M and that emitted by B.

Determine the time period of the system when $a$ is small.

Outline, without calculation, the change to the time period of the system for the model represented by graph B when $a$ is large.

A simple pendulum has a time period $T$ on the Earth. The pendulum is taken to the Moon where the gravitational field strength is $\frac{1}{6}$ that of the Earth.

What is the time period of the pendulum on the Moon?

A.  $T\sqrt{6}$

B.  $T$

C.  $\frac{\sqrt{6}}{6}T$

D.  $\frac{T}{6}$

In two different experiments, white light is passed through a single slit and then is either refracted through a prism or diffracted with a diffraction grating. The prism produces a band of colours from M to N. The diffraction grating produces a first order spectrum P to Q.

What are the colours observed at M and P?

Determine the amplitude of oscillation for test 1.

Deduce $\frac{k_1}{k_2}$.

The motion sensor operates by detecting the sound waves reflected from the base of the mass. The sensor compares the frequency detected with the frequency emitted when the signal returns.

The sound frequency emitted by the sensor is 35 kHz. The speed of sound is 340 m s⁻¹.

Determine the maximum frequency change detected by the sensor for test 2.

Calculate the frequency heard by the observer.

Show that, due to single slit diffraction, the intensity at a point on the screen a distance of 28 mm from M is zero.

An object at the end of a spring oscillates vertically with simple harmonic motion (shm). The graph shows the variation with time $t$ of the displacement $x$ of the object.

What is the velocity of the object?

A. $-\frac{2\pi A}{T}\sin \left(\frac{\pi t}{T}\right)$

B. $\frac{2\pi A}{T}\sin \left(\frac{\pi t}{T}\right)$

C. $-\frac{2\pi A}{T}\cos \left(\frac{\pi t}{T}\right)$

D. $\frac{2\pi A}{T}\cos \left(\frac{\pi t}{T}\right)$ 

Label on the graph with the letter X a point where the speed of the pendulum is half that of its initial speed.

The mass of the pendulum bob is 75 g. Show that the maximum speed of the bob is about 0.7 m s^–1.

The headlights of a car emit light of wavelength 400 nm and are separated by 1.2 m. The headlights are viewed by an observer whose eye has an aperture of 4.0 mm. The observer can just distinguish the headlights as separate images. What is the distance between the observer and the headlights?

A. 8 km

B. 10 km

C. 15 km

D. 20 km

A transparent liquid film of refractive index 1.5 coats the outside of a glass lens of higher refractive index. The liquid film is used to eliminate reflection from the lens at wavelength λ in air.

What is the minimum thickness of the liquid film coating and the phase change at the liquid–glass interface?

The four pendulums shown have been cut from the same uniform sheet of board. They are attached to the ceiling with strings of equal length.

Which pendulum has the shortest period?

An object undergoes simple harmonic motion (shm) of amplitude $x$₀. When the displacement of the object is $\frac{x_0}{3}$, the speed of the object is $v$. What is the speed when the displacement is $x$₀?

A. 0

B. $\frac{v}{3}$

C. $\frac{\sqrt{2}}{3}v$

D. $3v$

Light of wavelength λ is normally incident on a diffraction grating of spacing 3λ. What is the angle between the two second-order maxima?

A.  ${\sin }^{-1}\frac{2}{3}$

B.  ${\sin }^{-1}\frac{4}{3}$

C.  $2{\sin }^{-1}\frac{2}{3}$

D.  >90° so no second orders appear

calculate the smallest value of d that will result in destructive interference between ray X and ray Y.

Estimate, in rad, the smallest angular separation of two distinct point sources of light of wavelength 656 nm that can be resolved by the eye of this observer.

Predict whether reflected ray X undergoes a phase change.