Interference

State, with reference to the direction in which energy propagates, what is meant by a transverse wave.

Feb/March 2016

To show two-source interference of light, a light beam is divided into two beams by two slits $0.50\,\text{mm}$ apart. The two beams fall on a laboratory wall that is $4.0\,\text{m}$ away. The wavelength of the light is $550\,\text{nm}$. What is the separation of two neighbouring interference fringes produced on the laboratory wall?

Feb/March 2017

In a double-slit interference experiment, light with frequency $6.0 \times 10^{14}\ \text{Hz}$ falls on a pair of slits. On a screen placed some distance away, bright fringes spaced $3.0\ \text{mm}$ apart are seen. If the light frequency is altered to $5.0 \times 10^{14}\ \text{Hz}$, what is the new separation of the bright fringes?

Feb/March 2018

Monochromatic light falls on two narrow slits separated by $0.1\ \text{mm}$. A pattern of bright and dark fringes appears on a screen $2.0\ \text{m}$ away. The spacing between neighbouring bright fringes is $8.0\ \text{mm}$. What path difference exists between the light waves from the two slits at the second order dark fringe?

Feb/March 2018

Two identical loudspeakers are linked in series to an a.c. supply, as illustrated. A microphone is then moved along the line PQ. Which graph best shows how the intensity of the sound detected by the microphone varies with distance from P?

Feb/March 2019

Using two waves as your reference, state the principle of superposition.

Feb/March 2019

The table lists four possible sets of values for the laser wavelength, slit separation and slit-screen distance in a two-slit interference experiment, to demonstrate the interference of visible light on a white screen. Which set will produce visible fringes?

Feb/March 2020

Waves P and Q arrive together at point X and superpose. At first, the two waves reach X in phase (zero phase difference), giving a resultant wave amplitude of $14.0\,\text{cm}$ at that point. The phase difference between the two waves is then altered so that, at X, they have a phase difference of $180^\circ$. The resultant wave now has an amplitude of $4.0\,\text{cm}$ at X. What is the amplitude of one wave at point X?

Feb/March 2021

Microwave sources P and Q emit coherent waves that have a phase difference of $180^\circ$. Both waves share the same wavelength $\lambda$. At point S, the interference pattern formed by waves from the two sources shows a minimum. The distance $(QS - PS)$ is known as the path difference. Which expression could represent the path difference?

Feb/March 2021

Two coherent progressive waves arriving from separate sources overlap at one point. Which condition has to be met for the resultant amplitude to be zero at the point of overlap?

Feb/March 2022

Sound waves of wavelength $0.75\,\text{m}$ are produced in phase by two loudspeakers X and Y. As illustrated, an observer O can move to any position on a straight line through X and Y. O is located at a point where the waves arriving from X and Y are in phase. What could the distances OY and XY be?

Feb/March 2022

Two wave sources emit coherent waves. Which condition has to be satisfied for these waves to be coherent?

Feb/March 2024

A student carries out an experiment on double-slit interference. To illuminate a double slit, the student uses laser light with a single wavelength, and an interference fringe pattern is seen on the screen. The student observes that the fringes are very closely spaced. What could the student reduce to make the fringes farther apart on the screen?

Feb/March 2024

(a) A single-frequency coherent visible light beam is directed normally at a double slit. A bright-and-dark interference fringe pattern appears on a screen, as shown in Fig. 6.1.

Feb/March 2024

Light waves originate from two sources. What condition is required for observable interference fringes to form?

Feb/March 2025

When monochromatic light is used, an interference pattern of fringes appears on a screen that is positioned a distance $D$ from two slits separated by $a$. The fringe spacing is $x$. Now both $a$ and $D$ are doubled. What is the fringe spacing in the new pattern?

May/June 2010

With monochromatic light, interference fringes are formed on a screen located a distance $D$ from a pair of slits with separation $a$. The fringe spacing is $x$. Both $a$ and $D$ are then doubled. What will the new fringe separation be?

May/June 2010

When monochromatic light is used, interference fringes appear on a screen positioned a distance $D$ from a pair of slits separated by $a$. The fringe spacing is $x$. If both $a$ and $D$ are doubled, what is the new fringe separation?

May/June 2010

The diagrams illustrate how the apparatus is set up for a Young’s slits experiment, together with part of the pattern produced on the screen, with a ruler shown beside it. What wavelength does the light have?

May/June 2011

Explain what is meant by interference.

May/June 2011

The setup for generating interference fringes is illustrated in Fig. 6.1. It is not drawn to scale. Laser light falls on two slits. The laser emits light with only one wavelength. Light passing through the two slits forms a fringe pattern on the screen. A bright fringe appears at $C$ and the following bright fringe is at $B$. A dark fringe appears at $P$.

May/June 2011

A laser is used to create an interference pattern on a screen, as illustrated in Fig. 6.1. The laser emits light with wavelength $630\,\text{nm}$. The slit separation is $0.450\,\text{mm}$. The distance from the slits to the screen is $1.50\,\text{m}$. A maximum is produced at $P_1$ and a minimum is produced at $P_2$. Interference fringes are seen only when the light from the slits is coherent.

May/June 2012

Light with wavelength $600\,\text{nm}$ falls on a pair of slits, producing fringes that are spaced $4.0\,\text{mm}$ apart on a screen. What is the fringe spacing if the wavelength is changed to $400\,\text{nm}$ and the slit separation is doubled?

May/June 2013

Noise reduction headphones create their own sound waves to cancel external sound waves. Inside the headphones, a microphone detects waves of one frequency. A loudspeaker in the headphones then emits a wave with that same frequency but at a different phase. What phase difference is there between the external sound wave and the wave produced by the loudspeaker in the headphones?

May/June 2013

A teacher assembles the apparatus illustrated to show a two-slit interference pattern on the screen. Which modification to the apparatus would make the fringe spacing larger?

May/June 2013

State three conditions that have to be satisfied for maxima to be produced in an interference pattern formed by two sources of microwaves.

May/June 2013

Explain what the principle of superposition means.

May/June 2013

The principle of superposition states that a particular quantity is combined when two or more waves meet at a point. What is this quantity?

May/June 2014

The diagram illustrates an arrangement that has been assembled to show two-source interference. Microwaves with wavelength $\lambda$ travel through two slits $S_1$ and $S_2$. The detector is displaced away from point O in the direction shown by the arrow. The signal received falls until the detector arrives at point X, then rises again once the detector moves past X. Which equation gives the position of X correctly?

May/June 2014

A student tries to demonstrate light interference using two matching green LEDs. Which statement explains why this experiment will not work?

May/June 2014

A laser is set in front of a double slit, as shown in Fig. 7.1. The laser produces light with frequency $670\,\text{THz}$. Interference fringes appear on the screen.

May/June 2014

In a double-slit experiment, the separation of the fringes on a screen was too small to measure. What change would make the fringe spacing larger?

May/June 2015

The diagram shows two light waves with the same frequency. What might the phase difference be between these two waves?

May/June 2015

Which of the following is not a necessary condition for an interference pattern to be seen from waves coming from two sources?

May/June 2015

A wave pattern was seen even though the source of the waves could not be observed. The diagram shows the pattern. What can produce this pattern?

May/June 2015

At points X and Y, wave generators create water waves with identical wavelength. At Z, the waves arriving from X have the same amplitude as those arriving from Y. The distances XZ and YZ are shown. If the wave generators work in phase, the oscillation amplitude at Z is zero. What might the wavelength of the waves be?

May/June 2015

Two waves of the same type overlap while moving in the same direction. Fig. 6.1 shows how the displacement $y$ of each wave varies with distance $x$. The wave speed is $240\,\text{m s}^{-1}$. Since the waves are coherent, an interference pattern is formed.

May/June 2015

A screen $1.00\,\text{m}$ from a double slit shows fringes with spacing $x$ when the slits are illuminated by yellow light of wavelength $600\,\text{nm}$. At what distance from the slits should the screen be placed so that blue light of wavelength $400\,\text{nm}$ produces fringes with the same spacing $x$?

May/June 2016

Sound waves with wavelength $\lambda$ are produced by a loudspeaker and travel through two slits $P$ and $Q$. Two sound waves from these slits arrive together at $R$. What condition must be met for a microphone at $R$ to detect an intensity maximum (loud sound)?

May/June 2016

Coherent light is sent through a double slit, creating bright and dark fringes on a screen positioned parallel to the plane of the double slit. At first, the light intensity from each slit is equal. The intensity of the light passing through one slit in the double slit is then increased. The frequency of the light stays constant. What effect does this have on the appearance of the fringes on the screen?

May/June 2016

Which wave phenomenon is not required to account for the pattern of observable fringes formed in a double slit experiment?

May/June 2016

Figure 5.1 shows how the displacement y of wave X changes with time t as the wave passes point P. The intensity of wave X is I.

May/June 2016

An interference fringe pattern is formed with a red laser, a double slit and a screen. The screen is located $3.5\,\text{m}$ away from the double slit. The laser light has a wavelength of $640\,\text{nm}$. The fringe pattern is shown. What is the slit separation?

May/June 2017

Two wave sources vibrate in phase. Each source emits a wave with wavelength $\lambda$. At point X, the two waves arriving from the sources have a phase difference of $90^{\circ}$. What is one possible difference between the distances from the two wave sources to point X?

May/June 2017

Monochromatic light with wavelength $\lambda$ falls on two narrow slits $S_1$ and $S_2$, separated by a small distance. A sequence of bright and dark fringes appears on a screen far from the slits. The $n$th dark fringe away from the central bright fringe is seen at point P on the screen. Which equation is true for every positive value of $n$?

May/June 2017

Interference fringes can be seen when a laser light source illuminates a double slit. The double slit behaves as two light sources.

May/June 2017

A teacher arranges the apparatus shown to produce a double-slit interference pattern on the screen. Which modification to the apparatus will make the fringe spacing larger?

May/June 2018

In the diagram, two wave sources, $S_1$ and $S_2$, are shown. Their oscillations have a phase difference of $180^{\circ}$. Each source produces a wave with wavelength $2.0\,\text{cm}$. By the time the wave from each source reaches point $P$, its amplitude is $x_0$. What is the amplitude of the oscillation at $P$?

May/June 2018

The apparatus illustrated is used in a two-source interference experiment. What is the principal function of the single slit?

May/June 2018

A double-slit interference pattern produced with red light of wavelength $7.0 \times 10^{-7}\,\text{m}$ gives a fringe spacing of $3.5\,\text{mm}$. For the same arrangement of apparatus, what fringe spacing would be seen if blue light with wavelength $4.5 \times 10^{-7}\,\text{m}$ is used instead?

May/June 2018

State how the intensity of a wave is related to its amplitude.

May/June 2018

An interference experiment using a double slit is arranged as illustrated. Fringes appear on the screen. The separation between neighbouring bright fringes is measured as $4\,\text{mm}$. Two alterations are then made to the setup. The double slit is swapped for a different double slit with half the slit spacing. The screen is also shifted so that its distance from the double slit is twice as large. What is the new separation between neighbouring bright fringes?

May/June 2019

Why is it impossible to obtain a visible interference pattern between two monochromatic light beams from different lamps?

May/June 2019

A student arranges apparatus to observe double-slit interference using monochromatic light, as shown. Interference fringes appear on the screen. Which change would make the spacing between neighbouring fringes larger?

May/June 2019

Light with wavelength $\lambda$ is produced by two point sources R and S and reaches a screen far away. At point P on the screen, the light intensity is zero. What might account for the zero intensity at P?

May/June 2019

An apparatus setup is used to demonstrate double-slit interference with monochromatic light. The slit separation is $0.10\,\text{mm}$. The distance from the double slit to the screen on which the interference pattern is seen is $2.4\,\text{m}$, and the fringe width is $12\,\text{mm}$. The screen distance is then altered to $1.8\,\text{m}$ and the slit separation is doubled. What is the new fringe width?

May/June 2019

A loudspeaker vibrates with frequency f and produces sound waves of wavelength \lambda. The loudspeaker completes N oscillations in time t. State expressions, in terms of some or all of the symbols f, \lambda and N, for: (1) the distance travelled by a wavefront in time t, and (2) the time t.

May/June 2019

Monochromatic light of one wavelength is directed normally at two slits separated by $0.20\,\text{mm}$. Interference fringes are seen on a screen positioned $5.4\,\text{m}$ from the slits. The separation of adjacent bright fringes is $12\,\text{mm}$. What is the wavelength of the light?

May/June 2020

The diagram illustrates an arrangement set up to show two-source interference with coherent light of a single wavelength $\lambda$. An interference pattern is seen on a screen $3.0\,\text{m}$ from slits X and Y, and the slit separation is $1.0\,\text{mm}$. The central bright fringe is located at Q, and P is the second bright fringe from the centre. What is the separation between Q and P?

May/June 2020

A double-slit interference experiment is arranged with green light. Interference fringes are produced on a screen. Which one change would make the fringes farther apart?

May/June 2020

State, with reference to the direction in which energy is propagated, what a longitudinal wave means.

May/June 2020

Sources at points P and Q generate two identical waves. These waves follow different routes to arrive at point R, as illustrated. Each wave has a wavelength of $6.0\,\text{cm}$. At point R, the waves are in phase. What phase difference is there between the waves as they leave points P and Q?

May/June 2021

What wave behaviour does the diagram show?

May/June 2021

A teacher arranges the apparatus shown to show a double-slit interference pattern on a screen. Which alteration to the apparatus would make the fringe spacing larger?

May/June 2021

In a two-source interference experiment, light with a single frequency falls on a double slit. The light waves emerging from the slits are coherent. What does coherent mean?

May/June 2021

A double-slit interference pattern made with red light of wavelength $7.0 \times 10^{-7}\,\text{m}$ shows a fringe spacing of $3.5\,\text{mm}$. For the same arrangement of apparatus, what fringe spacing would be seen if blue light of wavelength $4.5 \times 10^{-7}\,\text{m}$ were used?

May/June 2021

For a progressive wave, state what the term period means.

May/June 2021

State what is meant by the principle of superposition.

May/June 2021

Monochromatic light passes through two narrow slits and forms an interference pattern on a screen positioned some distance away. The interference fringes are very close together. Which change would make the separation between the fringes larger?

May/June 2022

At an outdoor concert, there are two large speakers positioned next to the stage to project the music. To check the speakers, both are set to produce sound with the same wavelength and the same amplitude. The curved lines in the diagram show wavefronts. At which point is the sound loudest heard?

May/June 2022

The principle of superposition states that a particular quantity is combined when two or more waves meet at a point. What is this quantity?

May/June 2022

A beam of light from a laser falls normally on a double slit. Interference fringes are observed on a screen positioned parallel to the double slit. The slit separation is $a$. The gap between the slits and the screen is $D$. The spacing between the centres of two neighbouring bright fringes is $x$. $D$ and $a$ are both reduced by half. What is the spacing between the centres of two neighbouring bright fringes after these changes?

May/June 2022

A laser beam is directed onto two slits to create an interference pattern on a screen. Light with wavelength $660\,\text{nm}$ falls normally on slits separated by $0.44\,\text{mm}$. The screen is $1.8\,\text{m}$ from the double slit, measured perpendicular to it. The central bright fringe on the screen is at point O. The first dark fringe below O is at point P. The next bright fringe and the next dark fringe below P are at Q and R, respectively.

May/June 2022

A laser emits light with wavelength $650\,\text{nm}$. This beam is incident normally on two slits separated by $0.12\,\text{mm}$. A screen is set up parallel to the slits. The bright interference fringes on the screen are spaced $7.5\,\text{cm}$ apart. Determine the distance from the screen to the two slits.

May/June 2023

The diagram is a plan view of a double-slit interference demonstration. $L$ represents a monochromatic light source with a vertical filament. $B$ represents a barrier containing two narrow vertical slits, and $S$ represents a screen on which interference fringes appear. The intensity at the point on the screen at the centre of the fringe pattern is $I$. If one slit is covered, what intensity is found at that same point on the screen?

May/June 2023

Two coherent electromagnetic waves are moving through a vacuum. The two waves overlap at one point. At this point, the two waves have unequal intensities. Which statement about the waves is not correct?

May/June 2023

A wave of electromagnetic radiation travelling in a vacuum has a wavelength of $8.4 \times 10^{-6}\,\text{m}$.

May/June 2023

Microwaves are produced by two sources located at points X and Y. These two waves overlap at point Z. The diagram illustrates the routes taken by the two waves. The waves released from points X and Y are coherent. What direct effect does coherence between the two waves have?

May/June 2024

Interference fringes with spacing $x$ are seen on a screen placed $1.00\,\text{m}$ from a double slit illuminated by yellow light with wavelength $600\,\text{nm}$. At what distance from the double slit would fringes with the same spacing $x$ be produced if blue light of wavelength $400\,\text{nm}$ were used?

May/June 2024

Two waves overlap. This produces a resultant wave pattern. Which statement about the two waves has to be correct?

May/June 2024

A single-wavelength light beam is incident normally on a double slit. A pattern of interference fringes is seen on a screen. The separation between the double slit and the screen is $0.60\,\text{m}$, and the fringe spacing is $1.8\,\text{mm}$. If the distance between the double slit and the screen is increased by $0.90\,\text{m}$, what will the new fringe spacing be?

May/June 2025

Two sources, X and Y, produce electromagnetic waves with matching wavelengths. The waves from X and Y are emitted with a phase difference of $180^{\circ}$. A detector is moved along a route parallel to the line XY, where it records a sequence of intensity maxima and minima. The diagram illustrates the positions of the sources and the detector path. An intensity maximum is found at point Z. The distance XZ is $70\ \text{cm}$ and the distance YZ is $110\ \text{cm}$. What could be a possible wavelength of the waves?

May/June 2025

Two waves of the same kind overlap. At what point does the principle of superposition apply?

May/June 2025

Light of one frequency from two coherent sources produces alternating bright and dark fringes on a screen by interference. Which change would give a greater fringe separation?

May/June 2025

A laser beam of red light with a single wavelength is incident on a double slit. An interference fringe pattern is seen on a flat screen placed parallel to the double slit. Which change would increase the separation between the interference fringes on the screen?

May/June 2025

State what the principle of superposition means.

May/June 2025

A source vibrates at frequency $f$ to generate a progressive wave with wavelength $\lambda$. The source requires time $t$ to make $n$ full oscillations.

May/June 2025

A double slit experiment, carried out with light of wavelength $600 \text{ nm}$, produces fringes on a screen. The measured fringe separation is $1.0 \text{ mm}$. If the gap between the double slits and the viewing screen is increased by $2.0 \text{ m}$, the fringe separation rises to $3.0 \text{ mm}$. What is the separation of the double slits that gives rise to the fringes?

Oct/Nov 2010

State what is meant by the principle of superposition.

Oct/Nov 2010

The diagram gives a top view of a double slit interference experiment. L is a monochromatic light source with a vertical filament. B is a barrier containing two narrow vertical slits and S is a screen on which interference fringes are produced. The intensity is $I$ at the point on the screen where the centre of the fringe pattern is formed. What is the intensity, at that same point, when one slit is covered?

Oct/Nov 2011

Coherent waves originate at $P$ and at $Q$ and spread out in every direction. The line $RS$ lies halfway between $P$ and $Q$ and is perpendicular to the line joining $P$ and $Q$. The distance $RS$ is much greater than the distance $PQ$. Along which line, or lines, is an interference pattern seen?

Oct/Nov 2011

Visible interference fringes from two light sources are seen only under particular conditions. Which condition allows visible interference fringes to be produced?

Oct/Nov 2011

The diagram gives a plan view of a double-slit interference setup. $L$ is a monochromatic light source with a vertical filament. $B$ is a barrier containing two thin vertical slits and $S$ is a screen on which interference fringes are produced. The intensity is $I$ at a point on the screen where the centre of the fringe pattern is formed. What is the intensity, at that same point, when one slit is blocked?

Oct/Nov 2011

Coherent waves are generated at $P$ and at $Q$ and spread outwards in every direction. The line $RS$ lies midway between $P$ and $Q$ and is at right angles to the line joining $P$ and $Q$. The distance $RS$ is much larger than the distance $PQ$. On which line, or lines, can an interference pattern be seen?

Oct/Nov 2011

The diagram depicts two identical loudspeakers, both driven in phase by a shared audio-frequency source. As a student walks along line XY, he observes changes in the sound loudness. The sound is heard in alternating loud and quiet regions, as shown on the diagram. How may the separation between the loud regions be reduced?

Oct/Nov 2012

A student links two loudspeakers to a signal generator. As the student moves from P to Q, the loudness of the sound is seen to increase and decrease again and again. What causes the loudness of the sound to change?

Oct/Nov 2013

A student links two loudspeakers to a signal generator. While the student moves from P to Q, he observes that the loudness of the sound increases and decreases again and again. What makes the loudness of the sound change?

Oct/Nov 2013

In each diagram, the three waves have identical amplitude and frequency, but they are out of phase. When combined, they produce a resultant wave. For which case is the resultant wave zero?

Oct/Nov 2013

A student assembles apparatus to investigate double-slit interference of monochromatic light, as illustrated. Interference fringes appear on the screen. Which alteration would increase the spacing between neighbouring fringes?

Oct/Nov 2013

As illustrated, two identical loudspeakers are joined in series to an a.c. supply. Which graph most accurately shows how the intensity of the sound changes with distance along the line $XY$?

Oct/Nov 2014