Revision 1 Waves 10-05-16 - Hinchley Wood School

Revision 1 – Waves – 10-05-16 - Hinchley Wood School

Q1. (a) In an experiment, a narrow beam of white light from a filament lamp is directed at normal incidence at a diffraction grating. Complete the diagram in the figure below to show the light beams transmitted by the grating, showing the zero-order beam and the first-order beams.

(3)

(b) Light from a star is passed through the grating.

Explain how the appearance of the first-order beam can be used to deduce one piece of information about the gases that make up the outer layers of the star.

......

(2)

(c) In an experiment, a laser is used with a diffraction grating of known number of lines per mm to measure the wavelength of the laser light.

(i) Draw a labelled diagram of a suitable arrangement to carry out this experiment.

(2)

(ii)Describe the necessary procedure in order to obtain an accurate and reliable value for the wavelength of the laser light.
Your answer should include details of all the measurements and necessary calculations.
The quality of your written communication will be assessed in your answer.

......

(6)

(Total 13 marks)

Q2. (a) State the characteristic features of

(i)longitudinal waves,

......

(ii)transverse waves.

......

(3)

(b) Daylight passes horizontally through a fixed polarising filter P. An observer views the light emerging through a second polarising filter Q, which may be rotated in a vertical plane about point X as shown in Figure 1.

Figure 1

Describe what the observer would see as Q is rotated slowly through 360°.

You may be awarded marks for the quality of written communication provided in youranswer.

......

(2)

(Total 5 marks)

Q3. The diagram, which is not to scale, shows the cross-section of a 45° right angled glass prism supported by a film of liquid on a glass table. A ray of monochromatic light is incident on the prism at an angle of incidence θ and emerges along the glass - liquid boundary as shown.

refractive index of glass = 1.5

(a) Calculate the speed of light in the glass.

......

(2)

(b) Determine

(i)the angle of incidence, θ,

......

(ii)the refractive index of the liquid.

......

(5)

(c) The liquid is now changed to one with a lower refractive index. Draw a possible path for the ray beyond the point A and into the air.

(2)

(Total 9 marks)

Q4.Discuss the formation of stationary waves on a string or rope. Your account should include:

•alabelled diagram of a stationary wave

•the conditions necessary for stationary waves to form

•a definition of the terms node and antinode

•an explanation of how nodes and antinodes form.

The quality of written communication will be assessed in your answer.

(Total 6 marks)

Q5. A vertical screen is placed several metres beyond a vertical double slit arrangement illuminated by a laser. The diagram below shows a full-size tracing of the pattern of spots obtained on this screen. The black patches represent red light whilst the spaces between them are dark.

(a) Using the wave theory, explain how the pattern of bright and dark patches is formed.
You may be awarded marks for the quality of written communication provided in your answer.

......

(3)

(b) The slit separation was 0.90 mm and the distance between the slits and the screen was 4.2 m.

(i) Calculate the spacing of the bright fringes by taking measurements on the diagram of the tracing.

......

(ii) Hence determine the wavelength of the laser light used.

......

(4)

(Total 7 marks)

Q6. A single slit diffraction pattern is produced on a screen using a laser. The intensity of the central maximum is plotted on the axes in the figure below.

(a) On the figure above, sketch how the intensity varies across the screen to the right of the central maximum.

(2)

(b) A laser is a source of monochromatic, coherent light. State what is meant by

monochromatic light ......

......

coherent light ......

......

(2)

......

(1)

(d) State two ways in which the appearance of the fringes would change if the slit was made narrower.

......

(2)

(e) The laser is replaced with a lamp that produces a narrow beam of white light. Sketch and label the appearance of the fringes as you would see them on a screen.

(3)

(Total 10 marks)

Q7.Figure 1 shows a side view of a string on a guitar. The string cannot move at either of the two bridges when it is vibrating. When vibrating in its fundamental mode the frequency of the sound produced is 108 Hz.

(a) (i) On Figure 1, sketch the stationary wave produced when the string is vibrating in its fundamental mode.

Figure 1

(1)

(ii) Calculate the wavelength of the fundamental mode of vibration.

answer = ...... m

(2)

(iii) Calculate the speed of a progressive wave on this string.

answer = ...... m s–1

(2)

(b) While tuning the guitar, the guitarist produces an overtone that has a node 0.16 m from bridge A.

(i) On Figure 2, sketch the stationary wave produced and label all nodes that are present.

Figure 2

(2)

(ii) Calculate the frequency of the overtone.

answer = ...... Hz

(1)

(c) The guitarist needs to raise the fundamental frequency of vibration of this string.
State one way in which this can be achieved.

......

(1)

(Total 9 marks)

M1. (a)max three from

central maximum shown

two equally spaced first order maxima

central and one first order labelled correctly

central white maximum

indication of spectra/colours in at least one first order beam

at least one first order beam labelled with violet (indigo or blue) closest to the
centreor red furthest

(b) dark/black lines or absorption spectrum orFraunhofer lines

(reveal the) composition (of the star’s atmosphere)

accept dark ‘bands’

accept atoms or elements in the star

or the peak of intensity

(is related to) the temperature

or Doppler (blue or red) shift

(speed of) rotation or speed of star (relative to Earth)

(c)(i)grating and screen shown with both labelled

laser or laser beam labelled

(ii)The candidate’s writing should be legible and the spelling, punctuation
and grammar should be sufficiently accurate for the meaning to be clear.

The candidate’s answer will be assessed holistically. The answer will be
assigned to one of three levels according to the following criteria.

High Level (Good to excellent): 5 or 6 marks

The information conveyed by the answer is clearly organised, logical and
coherent, using appropriate specialist vocabulary correctly. The form and style
of writing is appropriate to answer the question.

•correct use of (n)λ = d sin θ

•and measure appropriate angle (eg‘to first order beam’ is the minimum required)

•and method to measure angle (eg tan θ = x/D, spectrometer, accept protractor)

•and at least one way of improving accuracy/reliability

•forfull marks: also explain how d is calculated, egd = 1/ lines per mm
(× 103)

Intermediate Level (Modest to adequate): 3 or 4 marks

The information conveyed by the answer may be less well organised and not
fully coherent. There is less use of specialist vocabulary, or specialist
vocabulary may be used incorrectly. The form and style of writing is less
appropriate.

•use of (n)λ= d sin θ

•and measure appropriate angle (eg‘to first order beam’ is the minimum required)

•and method of measurement of θ (eg tan θ = x/D, spectrometer, accept protractor) or at least one way of improving accuracy/reliability

Low Level (Poor to limited): 1 or 2 marks

The information conveyed by the answer is poorly organised and may not be
relevant or coherent. There is little correct use of specialist vocabulary. The form
and style of writing may be only partly appropriate.

•use of (n)λ = d sin θ

•or measure appropriate angle (eg‘to first order beam’ is the minimum required)

•or at least one way of improving accuracy/reliability

Incorrect, inappropriate of no response: 0 marks

No answer or answer refers to unrelated, incorrect or inappropriate physics.

The explanation expected in a competent answer should include

Accuracy/reliability points

•measure between more than one order (eg 2 θ)

•measureθ for different orders (for average λnot average angle)

•check or repeat/repeat for different distances (D)

•use of spectrometer

•use large distance to screen (D)

•protractor with 0.5 degree (or less) intervals

•graphical method: plot sin θ against n (gradient = λ/d)

[13]

M2. (a) (i) particle vibration (or disturbance or oscillation) (1)
same as (or parallel to) direction of propagation
(or energy transfer) (1)

(ii) (particle vibration)
perpendicular to direction of propagation (or energy transfer) (1)

(b)variation in intensity between max and min (or light and dark) (1)
two maxima (or two minima) in 360° rotation (1)

QWC 1

[5]

M3. (a)cg (= ) = (1)

= 2.0 × 108 m s–1(1)

(b) (i) sin 1 (= n sin 2) = 1.5 × sin 15 (1)
1 = 23° (1) (22.8°)

(ii)use of (1) (or equivalent)

n2 = (1)

= 1.3 (1)

(c)total internal reflection at A (1)
correct refraction out of glass at r.h.
surface (1) (same angles as l.h. side)

[9]

M4.Good / Excellent

The candidate’s writing should be legible and the spelling, punctuation and grammar should be sufficiently accurate for the meaning to be clear.
The candidate’s answer will be assessed holistically. The answer will be assigned to one of three levels according to the following criteria.

High Level (Good to excellent): 5 or 6 marks
The information conveyed by the answer is clearly organised, logical and coherent, using appropriate specialist vocabulary correctly. The form and style of writing is appropriate to answer the question.

can say disturbance, amplitude or displacement

Mentions:

•(1) waves (meet when) travelling in opposite directions / cross/ wave meets a reflected wave / etc

•(2) same wavelength (or frequency)

•(3) node– point of minimum or no disturbance

•(4) antinode– point of maximum disturbance / maximum displacement/amplitude occurs

•(5) node - two waves (always) cancel / destructive interference / 180o phase difference (between displacements of the two waves at the node)

•(6) antinode– reinforcement / constructive interference occurs / (displacements) in phase

•(7) mention of superposition of the two waves

5 marks: points (1) AND (2) with three points from (3), (4), (5), (6) or (7)

for 6 marks: points (1) to (6) must be seen

labelled diagram can provide
supporting evidence but labels: ‘node’ / ‘antinode’ by themselves cannot replace points 3 and 4

5 / 6

Modest
Intermediate Level (Modest to adequate): 3 or 4 marks
The information conveyed by the answer may be less well organised and not fully coherent. There is less use of specialist vocabulary, or specialist vocabulary may be used incorrectly. The form and style of writing is less appropriate.

Mentions any 3 of the 7 points.

4 marks: (1) OR (2) AND three others.

3 / 4

Limited
Low Level (Poor to limited): 1 or 2 marks
The information conveyed by the answer is poorly organised and may not be relevant or coherent. There is little correct use of specialist vocabulary. The form and style of writing may be only partly appropriate.

One relevant point

OR a relevant, labelled diagram

2 marks: two points OR one point and a relevant labelled diagram

1 / 2

[6]

M5. (a)slits act as coherent sources (1)
waves/light diffract at slits (1)
waves overlap/superpose/meet/cross (1)
bright patches : constructive/waves in phase/reinforce (1)
dark patches : destructive/waves out of phase/cancel (1)

max 3

QWC 2

(b) (i) spacing w== 3.0 or 2.9 mm (1) (2.92 ± 0.04 mm)

15 or more fringes used (1)

(ii) (use of λ = gives)λ = (1)

= 6.26 × 10‑7

(allow C.E. for sensible value of w from (i))

[7]

M6. (a) 3 subsidiary maxima in correct positions (1)

intensity decreasing (1)

(b)a single wavelength (1)

constant phase relationship/difference (1)

(c)maxima further apart/central maximum wider/subsidiary maximum
wider/maxima are wider (1)

(d) wider/increased separation (1)

lower intensity (1)

(e)distinct fringes shown with subsidiary maxima (1)

indication that colours are present within each subsidiary maxima (1)

blue/violet on the inner edge or red outer for at least one subsidiary
maximum (1)

(middle of) central maximum white (1)

[10]

M7. (a) (i) one ‘loop’ (accept single line only, accept single dashed line)

+ nodes at each bridge (± length of arrowhead)

+ antinode at centre (1)

(ii)λ0 = 2L or λ= 0.64 × 2 (1)

= 1.3 (m) (1) (1.28)

(iii) (c = f λ) = 108 × (a)(ii) (1)

= 138 to 140(.4) (m s–1) (1)ecf from (a) (ii)

(b) (i) four antinodes (1) (single or double line)

first node on 0.16 m (within width of arrowhead)

+ middle node between the decimal point and the centre of the
‘m’ in ‘0.64 m’

+ middle 3 nodes labelled‘N’, ‘n’ or ‘node’ (1)

(ii) (4 f0 =) 430 (Hz) (1) (432)

or use of f = gives 430 to 440 Hz correct answer only, no ecf

(c)decrease the length/increase tension/tighten string (1)

[9]

E1. Part (a) was done well by most students. However, many would have benefitted from using a protractor to get the angles between the zero order and the two first-order beams roughly equal.

In part (b), the basic requirement is that students know that dark lines (absorption lines) are seen on the spectra from stars and that these reveal elements present in the outer layers of the star. The mark scheme also credited other uses of a stars spectrum. Many students had the idea that spectral lines revealed elements but few knew about absorption lines. This is an area where students who have taken PHYA1 first may have an advantage since they have studied atomic energy levels and may have seen absorption spectra.

Labelling a laser, diffraction grating and some sort of screen or suitable detector was all that was required for the two marks in part (c) (i). Many students missed out the screen. Some had double slits instead of a grating.

Part (c) (ii) was, in general, poorly answered. Many students did not seem to be familiar with this practical and instead described a two-slit approach to measuring wavelength. Those who seemed familiar with the procedure tended not to fully answer the question which asked for details of all the measurements and necessary calculations. The candidate who leaves out these details is unlikely to be able to score more than two marks out of six even if they have given a reasonable general description of the experiment. For example, they must include details of how the angle is to be measured eg by measuring the distance between the zero order and the first-order beam (using a ruler) and the distance between the screen and the grating. They must then use tan θ = O/A to calculate the angle. Where students knew which equation to use, they tended to know insufficient detail to score more than a few marks. Of those students who did describe the use of a grating, many did not know the meanings of the symbols in the equation eg, d was often thought to be the distance between grating and screen and n, the number of lines per mm or even the refractive index of air. Many described measuring the grating spacing with micrometers or metre rules, forgetting that the question stated that the lines per mm are known.

In short, many of the students who took this exam seemed poorly prepared for this type of question. They were, in some cases, able to produce an answer from a past paper for a closely related, but significantly different, question. Many seemed unaware of the style and quality of answer expected.

Most answers were vague, the literacy level was generally poor and there was a lack of detail regarding the measurements and what should be done with them. This is often the case in the January examination, but it is possible to improve the necessary skills even in the short preparation time available. A few structured lessons on answering this type of question can to be incorporated into schemes of work, allowing students to be fully aware of the expectations.

E2. Reluctance to memorise conventional definitions meant that many candidates were struggling to construct an answer in part (a). This usually caused a failure to express ideas sufficiently clearly for any marks to be awarded - for example “the waves move along in the same direction as the wave is travelling”. Part (b) was generally very well answered, although there were references to coloured effects and/or fringes in some scripts. The most frequent mistake amongst more successful candidates was the notion that successive maxima of intensity occurred every 360° of rotation, rather than every 180°.

E3. The optics question again seems to be the Achilles heel of most candidates and the calculation of the speed of light in part (a) was practically the only section that was done well.

The calculation of è in part (b) (i) was incorrect in about a third of cases because Snell’s law equation was inverted when data was substituted. Only a minority of candidates seemed to be able to cope with calculations involving more than one refractive index, as was required in part (b) (ii). It was extremely common to see

candidates attempting to use the equation at the glass-liquid boundary,

which was wrong on two levels. Firstly it ignored the refractive index of the glass, and also the critical angle calculated was not the critical angle for the material for which the refractive index was required. When it came to drawing the path of the ray, there were more incorrect solutions than correct ones. Most candidates drew the ray passing down through the liquid and ignored total internal reflection altogether.

E4.This was a very accessible question given that there are several past paper questions that address the same issue of the formation of stationary waves.

Candidates did very well on this question but there was a lack of understanding of some wave terminology evident. Candidates often correctly explained that two progressive waves travelling in opposite directions give rise to a stationary wave. However, they often described the waves as having a constant phase difference and being coherent. Many also thought that a node is formed by a peak cancelling a trough and an antinode is formed by a peak meeting peak or a trough meeting a trough.

An antinode is formed at a position where the displacements of the two waves are always in the same direction and of equal magnitude, they are not always peaks or troughs. A node is formed where the waves always cancel and this is not only due to a peak meeting a trough but is due to the waves having equal and opposite displacements at the position of the node. Another common misconception was that two troughs meet to give destructive interference.

The two progressive waves have a constantly varying phase difference. It would be correct to say that at the position of a node, the two waves are always in antiphase and they arrive at antinode in phase.

E5. Although some candidates thought part (a) was about the diffraction grating, the majority gave good explanations of the double slit interference pattern. However, limitations over the use of English caused difficulty in some scripts, where it was the laser that was passed through the double slit system! Examiners were expecting to see references to waves diffracting from the two coherent sources provided by the slits, then overlapping to produce constructive and destructive interference effects on the screen. ‘Destructive’ sometimes became‘deconstructive’, and there were frequent incorrect references to a phase difference of nλ. Another common misunderstanding was that two troughs combine to give minimum displacement.