Question
Blue light of wavelength \(\lambda\) is incident on a double slit. Light from the double slit falls on a screen. A student measures the distance between nine successive fringes on the screen to be \(15 \mathrm{~cm}\).
The separation of the double slit is \(60 \mu \mathrm{m}\); the double slit is \(2.5 \mathrm{~m}\) from the screen.
(a) Explain the pattern seen on the screen. [3]
(b) Calculate, in \(\mathrm{nm}, \lambda\). [3]
(c) The student changes the light source to one that emits two colours:
- blue light of wavelength \(\lambda\), and
- red light of wavelength \(1.5 \lambda\).
Predict the pattern that the student will see on the screen.[3]
▶️Answer/Explanation
Ans:
a. Mention of interference / superposition
Bright fringe occurs when light from the slits arrives in phase
Dark fringe occurs when light from the slits arrives \(180 \% \pi\) out of phase \(\checkmark\)
b $
s=\frac{0.15}{8} O R=0.0188 \ll \mathrm{mm}
$
use of \(\lambda=\frac{d s}{D}\)
450 «nm» \(\checkmark\)
c.Blue fringe is unchanged \(\checkmark\)
Red fringes are farther apart than blue
By a factor of \(1.5 \checkmark\)
At some point/s the fringes coincide/are purple
Question
This question is in two parts. Part 1 is about simple harmonic motion (SHM) and sound. Part 2 is about electric and magnetic fields.
Part 1 Simple harmonic motion (SHM) and sound
The diagram shows a section of continuous track of a long-playing (LP) record. The stylus (needle) is placed in the track of the record.
As the LP record rotates, the stylus moves because of changes in the width and position of the track. These movements are converted into sound waves by an electrical system and a loudspeaker.
A recording of a single-frequency musical note is played. The graph shows the variation in horizontal acceleration of the stylus with horizontal displacement.
Sound is emitted from a loudspeaker which is outside a building. The loudspeaker emits a sound wave that has the same frequency as the recorded note.
A person standing at position 1 outside the building and a person standing at position 2 inside the building both hear the sound emitted by the loudspeaker.
A, B and C are wavefronts emitted by the loudspeaker.
Part 2 Electric and magnetic fields
Electrical leads used in physics laboratories consist of a central conductor surrounded by an insulator.
Explain why the graph shows that the stylus undergoes simple harmonic motion.
(i) Using the graph on page 14, show that the frequency of the note being played is about 200 Hz.
(ii) On the graph on page 14, identify, with the letter P, the position of the stylus at which the kinetic energy is at a maximum.
(i) Draw rays to show how the person at position 1 is able to hear the sound emitted by the loudspeaker.
(ii) The speed of sound in the air is . Calculate the wavelength of the note.
(iii) The walls of the room are designed to absorb sound. Explain how the person at position 2 is able to hear the sound emitted by the loudspeaker.
The arrangement in (c) is changed and another loudspeaker is added. Both loudspeakers emit the same recorded note in phase with each other.
Outline why there are positions between the loudspeakers where the sound can only be heard faintly.
Distinguish between an insulator and a conductor.
The diagram shows a current I in a vertical wire that passes through a hole in a horizontal piece of cardboard.
On the cardboard, draw the magnetic field pattern due to the current.
(i) The diagram shows a length of copper wire that is horizontal in the magnetic field of the Earth.
The wire carries an electric current and the force on the wire is as shown. Identify, with an arrow, the direction of electron flow in the wire.
(ii) The horizontal component of the magnetic field of the Earth at the position of the wire is
Answer/Explanation
Markscheme
acceleration is proportional to displacement;
force/acceleration is directed towards equilibrium (point)/rest position; } (do not accept “centre” or “fixed” point)
straight line through the origin shows the proportionality;
negative gradient shows acceleration directed towards equilibrium (point) / acceleration has opposite sign to displacement;
(i) gradient;
Allow substitution for fourth mark.
(ii) at origin;
(i) ray shown at 90° to wavefront A, plausible reflection and reflected ray goes in direction of position 1; } (judge by eye)
(ii) 1.65 (m); (allow ECF from (b)) (accept rounding to 1.6 or 1.7)
(iii) mention of diffraction;
diffraction means that sound spreads beyond the limit of geometrical shadow/can go around a corner / OWTTE;
Accept marking points in the form of a clearly drawn correctly labelled diagram.
interference/superposition mentioned;
when sounds arrive out of phase / path difference half integer number of wavelengths / OWTTE;
cancellation occurs / destructive (interference);
some (back) reflection from walls so cancellation may not be complete (hence “faint” not “zero”);
conductor has free electrons/charges that are free to move within/through it / insulator does not have free electrons/charges that are free to move within/ through it;
electrons act as charge carriers;
when a pd acts across a conductor a current exists when charge (carriers) move;
Do not allow “good/bad conductor/resistor” or reference to conductivity/resistivity.
anti-clockwise arrows;
at least three circles centred on wire;
increasing in separation from centre;
(i) arrow to the right;
(ii)
35 (A);
Award [3] for a bald correct answer.
Allow use of g = 10 m
“>
s–2 which also gives an answer of 35 (A).
Examiners report
It was rare to see all four marks awarded for statements of the requirements of harmonic oscillation and recognition of these in the straight-line graph. Candidates were generally happy to state that acceleration is directly proportional to displacement and that the straight line through the origin confirmed this. Correct statements with appropriate detail of the direction of the force/acceleration were rarer and the negative gradient was not often mentioned. Four marks were available and therefore candidates should have recognised that four points were required.
(i) This calculation was poorly done.
(ii) P – when it was marked on the graph at all – was either shown at the origin (correct) or one extreme (incorrect) of the graph in about equal numbers.
(i) Candidates are required to know the relationship between wavefronts and rays and it was surprising that many completed the diagram with wavefronts – and even these would not have gained much credit given the very poor draughtsmanship in evidence. Few candidates bothered to read the question. They failed to realise that all they were required to do was construct plausible incident and reflected rays that would enable the observer at point 1 to hear the sound.
(ii) There were many examples of correct evaluation of the wavelength of the sound but far too many were unable to complete this simple task. Inversions of the equation and mistakes in powers of ten and in rounding were common.
(iii) The usual phonetic spelling of “defraction” was observed. Examiners are unlikely to give a benefit of the doubt to what might have been a phonetic spelling or might equally have been confusion with “refraction” in this particular case. Many candidates were able to spot that the sound was being diffracted but an explanation of what diffraction is, in context, was much rarer.
[N/A]
Superficial answers were common. Candidates continue to ignore the mark allocations for questions and therefore the number of independent points they should mention in an answer. Here, most said that conductors contain free electrons (or the reverse for insulators) but did not go on to discuss the role of the free electrons in carrying charge or to relate the current to the existence of an electric field across the conductor. Far too many gave answers of the “conductors conduct well” variety that do not score marks.
There are three elements to a good drawing of the magnetic field around a long straight conductor: the concentric circularity of the lines, the direction of the lines related to the direction of charge flow, and the increasing separation between lines as the distance from the conductor increases. It was a rare candidate who was able to convince the examiner with all three points. In hindsight, the diagram could have been larger on the page. However, candidates could have taken more trouble over their sketches which were usually crude.
(i) Many forgot that the sign rules involve conventional current and lost the mark.
(ii) Few correct solutions were observed. This was a straightforward problem involving one re-arrangement of a standard equation and the incorporation of the weight of the conductor.
This question is in two parts. Part 1 is about a lightning discharge. Part 2 is about microwave radiation.
Part 2 Microwave radiation
A microwave transmitter emits radiation of a single wavelength towards a metal plate along a line normal to the plate. The radiation is reflected back towards the transmitter.
A microwave detector is moved along a line normal to the microwave transmitter and the metal plate. The detector records a sequence of equally spaced maxima and minima of intensity.
The microwave detector is moved through 130 mm from one point of minimum intensity to another point of minimum intensity. On the way it passes through nine points of maximum intensity. Calculate the
Part2.a.
Explain how these maxima and minima are formed.
(i) wavelength of the microwaves.
(ii) frequency of the microwaves.
Describe and explain how it could be demonstrated that the microwaves are polarized.
Answer/Explanation
Markscheme
Part2.a.
standing wave formed;
by superposition/interference of (forward) wave and reflected wave;
maximum where interference is constructive / minimum where interference is destructive;
maxima where waves in phase;
minima where waves are completely/180°/\(\pi \)/half wavelength out of phase;
(i) \({\text{130 mm}} \equiv {\text{9 half wavelengths}}\);
29 mm;
(ii) \(f = \frac{c}{\lambda }\);
\( = 10{\text{ GHz}}\);
place a metal grid/analyser between source and detector;
electric field vector (of the microwaves) vibrates in only one direction/plane;
rotate the metal grid/detector;
until minimum signal is detected;
or
electric field vector vibrates in only one direction/plane;
rotate transmitter through an angle;
need to rotate receiver through same angle to restore signal in transmitter;
Examiners report
Part2.a.
Few were able to give complete and convincing explanations of the formation of the standing wave. Common errors were to omit the consequence of the reflection at the metal plate. Superposition was often poorly or even not described. Details of the phase relationships were also poor.
(i) and (ii) Candidates were very comfortable with these calculations although the number of wavelengths in (i) was often incorrect. Errors from (i) were carried forward to (ii) allowing many cases of full credit in this second part.
Examiners saw very few good descriptions of the polarization demonstration. A number of techniques are available but it is clear that candidates have either not discussed these or find the concept difficult.