Wave Final

8/17/2019 Wave Final

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Wave & Oscillation

AS level

1 The variation with time t of the displacement x of a point in a transverse wave T1 is

shown in Fig. 1.1.

Fig. 1.1

(a) By reference to displacement and direction of travel of wave energy, explain what is

meant by a transverse wave........................................................................................................................................

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[1](b) A second transverse wave T, of amplit!de A has the same waveform as wave T1 b!tlags behind T1 by a phase angle of "#$. The two waves T1 and T pass thro!gh the

same point.

(i) %n Fig. 1.1, draw the variation with time t of the displacement x of the point inwave T.

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(ii) &xplain what is meant by the principle of superposition of two waves...................................................................................................................................

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(iii) For the time t ' 1.# s, !se Fig. 1.1 to determine, in terms of A,1. the displacement d!e to wave T1 alone,

displacement ' ((((((((((((((.

2. the displacement d!e to wave T alone,

displacement ' ((((((((((((((.

3. the res!ltant displacement d!e to both waves.

displacement ' ((((((((((((((.[)]


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2


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3 The spectr!m of electromagnetic waves is divided into a n!mber of regions s!ch as radio waves, visible

light and gamma radiation.

(a) *tate three distinct feat!res of waves that are common to all regions of the

&lectromagnetic spectr!m.

1..........................................................................................................................................................................................................................................................................

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[)](b) A typical wavelength of visible light is +- nm. alc!late the n!mber of wavelengths of this light in a

wave of length 1.##m.

/!mber ' ((((((((((.[]

(c) *tate a typical wavelength for (i) 0rays,

wavelength ' ((((((((((. m(ii) infrared radiation.

2avelength ' ((((((((((. 3

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4 A string is stretched between two fixed points. 4t is pl!c5ed at its centre and the string vibrates, forming a

stationary wave as ill!strated in Fig. +.1.

Fig. 4.1

The length of the string is 6- cm.(a) *tate the wavelength of the wave.

wavelength ' ((((((((((. m[1]

(b) The fre7!ency of vibration of the string is )"# 89. alc!late the speed of the wave on the string.

speed ' ((((((((((( ms :1

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(c) By reference to the formation of the stationary wave on the string, explain what is meant by the speed

calc!lated in (b).

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[)]

5 Fig. -.1 shows the variation with time t of the displacements xA and xB at a point ; of two so!nd waves A

and B.

Fig. 5.1

(a) By reference to Fig. -.1, state one similarity and one difference between these two waves.


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similarity


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lines per millimetre, as ill!strated in Fig. ".1.

Fig. 6.1

?ed light of wavelength @ is also incident normally on the grating. The first order diffracted light of both wavelengths is ill!strated in Fig. ".1.

(i) alc!late the n!mber of orders of diffracted light of wavelength "++ nm that are

visible on each side of the 9ero order.

n!mber ' (((((((((( [+](ii) *tate and explain

1. whether @ is greater or smaller than "++ nm,

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[1]2. in which order of diffracted light there is the greatest separation of the two

wavelengths.

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7 (a) Fig. 6.1 shows the variation with time t of the displacement y of a wave 2 as it passes a point ;. The wave has intensity I .

Fig. 7.1

A second wave 0 of the same fre7!ency as wave 2 also passes point ;.

This wave has intensity I . The phase difference between the two waves is "#$.%n Fig. 6.1, s5etch the variation with time t of the displacement y of wave 0.


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[)](b) 4n a do!bleslit interference experiment !sing light of wavelength -+# nm, the separation

of the slits is #.6## mm. The fringes are viewed on a screen at a distance of .6- m from

the do!ble slit, as ill!strated in Fig. 6. not to scaleC.

Fig. 7.2

alc!late the separation of the fringes observed on the screen.

separation ' ................................ mm [)]

(c) *tate the effect, if any, on the appearance of the fringes observed on the screen when

the following changes are made, separately, to the do!bleslit arrangement in (b).

(i) The width of each slit is increased b!t the separation remains constant.

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[)](ii) The separation of the slits is increased..................................................................................................................................

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8 (a) &xplain what is meant by the diffraction of a wave.

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(b) (i) %!tline briefly an experiment that may be !sed to demonstrate diffraction of a

transverse wave.

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[)]

(ii) *!ggest how yo!r experiment in (i) may be changed to demonstrate the diffraction

of a longit!dinal wave.


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[)] (a) *tate what is meant by a progressive wave.

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[](b) The variation with distance x along a progressive wave of a 7!antity y, at a partic!lar

time, is shown in Fig. .1.

Fig. .1

(i) *tate what the 7!antity y co!ld represent..................................................................................................................................

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(ii) >isting!ish between the 7!antity y for 1. a transverse wave,

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2. a longit!dinal wave.

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(c) The wave nat!re of light may be demonstrated !sing the phenomena of diffraction and

interference.

%!tline how diffraction and how interference may be demonstrated !sing light.

4n each case, draw a f!lly labeled diagram of the apparat!s that is !sed and describe

what is observed.

diffraction

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interference

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["]1! A !niform string is held between a fixed point ; and a variablefre7!ency oscillator, as shown

in Fig. 1#.1.

Fig. 1!.1


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The distance between point ; and the oscillator is L.

The fre7!ency of the oscillator is adD!sted so that the stationary wave shown in Fig. 1#.1 is formed.

;oints 0 and E are two points on the string.

;oint 0 is a distance 1G L from the end of the string attached to the oscillator. 4t vibrates with fre7!ency fand amplit!de A.

;oint E is a distance 1G L from the end ; of the string.

(a) For the vibrations of point E, state

(i) the fre7!ency in terms of f C,

fre7!ency ' ................................................

[1](ii) the amplit!de in terms of AC.

amplit!de ' ................................................

[1](b) *tate the phase difference between the vibrations of point 0 and point E.

phase difference ' ................................................

[1]

(c) (i) *tate, in terms of f and L, the speed of the wave on the string.

speed ' ................................................

[1](ii) The wave on the string is a stationary wave.

&xplain, by reference to the formation of a stationary wave, what is meant by the

speed stated in (i).

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[)]11 (a) Figs. 11.1aC and bC show plane wave fronts approaching a narrow gap and a wide gap

respectively.


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Fig. 11.1

%n Figs. 11.1aC and bC, draw three s!ccessive wave fronts to represent the wave after it

has passed thro!gh each of the gaps.[-]

(b) Hight from a laser is directed normally at a diffraction grating, as ill!strated in Fig. 11..

Fig. 11.2

The diffraction grating is sit!ated at the centre of a circ!lar scale, mar5ed in degrees.The readings on the scale for the second order diffracted beams are 1)"$ and 1"$.

The wavelength of the laser light is ")# nm.

alc!late the spacing of the slits of the diffraction grating.

spacing ' ............................................... m [+]

(c) *!ggest one reason why the fringe pattern prod!ced by light passing thro!gh adiffraction grating is brighter than that prod!ced from the same so!rce with a do!ble slit.

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[1]

12


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13 Fig. 1).1 shows the variation with distance x along a wave of its displacement d at a partic!lar

time.

Fig. 13.1

The wave is a progressive wave having a speed of ))#ms :1.

(a) (i) Ise Fig. 1).1 to determine the wavelength of the wave.

wavelength ' ................................... m

(ii) 8ence calc!late the fre7!ency of the wave.

fre7!ency ' .................................... 89

[)](b) A second wave has the same fre7!ency and speed as the wave shown in Fig. 1).1 b!t

has do!ble the intensity. The phase difference between the two waves is 1G#$.

%n the axes of Fig. 1).1, s5etch a graph to show the variation with distance x of the

displacement d of this second wave.[]


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14 (a) &xplain what is meant by the diffraction of a wave.

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(b) Hight of wavelength -# nm is incident normally on a diffraction grating having 6-# lines

per millimeter.

The diffraction grating form!la may be expressed in the form

d sinJ ' n@.

(i) alc!late the val!e of d , in meters, for this grating.

d ' ............................................. m

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(ii) >etermine the maxim!m val!e of n for the light incident normally on the grating.

maxim!m val!e of n ' .................................................[]

(iii) Fig. 1+.1 shows incident light that is not normal to the grating.

Fig. 14.1

*!ggest why the diffraction grating form!la, d sinJ ' n@, sho!ld not be !sed in this

sit!ation...................................................................................................................................

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[1](c) Hight of wavelengths -# nm and -- nm is now incident normally on the grating.Two lines are observed in the first order spectr!m and two lines are observed in the

second order spectr!m, corresponding to the two wavelengths.*tate two differences between the first order spectr!m and the second order spectr!m.

1...............................................................................................................................................................................................................................................................................

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[]15 A long t!be, fitted with a tap, is filled with water. A t!ning for5 is so!nded above the top of the

t!be as the water is allowed to r!n o!t of the t!be, as shown in Fig. 1-.1.


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Fig. 15.1 Fig. 15.2

A lo!d so!nd is first heard when the water level is as shown in Fig. 1-.1, and then again when

the water level is as shown in Fig. 1-..

Fig. 1-.1 ill!strates the stationary wave prod!ced in the t!be.

(a) %n Fig. 1-.,

(i) s5etch the form of the stationary wave set !p in the t!be,

[1]

(ii) mar5, with the letter /, the positions of any nodes of the stationary wave.[1]

(b) The fre7!ency of the for5 is -189 and the difference in the height of the water level for

the two positions where a lo!d so!nd is heard is ).+ cm.

alc!late the speed of so!nd in the t!be.

speed ' (((((((( ms :1

[)]

(c) The length of the col!mn of air in the t!be in Fig. 1-.1 is 1-.6 cm.*!ggest where the antinode of the stationary wave prod!ced in the t!be in Fig. 1-.1 is

li5ely to be fo!nd.

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16 Hight reflected from the s!rface of smooth water may be described as a polari9ed transverse

wave.(a) By reference to the direction of propagation of energy, explain what is meant by

(i) a transverse wave,

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.............................................................................................................................. [1](ii) polarisation.

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[1](b) A glass t!be, closed at one end, has fine d!st sprin5led along its length. A so!nd so!rce

is placed near the open end of the t!be, as shown in Fig. 1".1.

Fig. 16.1

The fre7!ency of the so!nd emitted by the so!rce is varied and, at one fre7!ency, the

d!st forms small heaps in the t!be.

(i) &xplain, by reference to the properties of stationary waves, why the heaps of d!stare formed.

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[)](ii) %ne fre7!ency at which heaps are formed is .1+ 589.

The distance between six heaps, as shown in Fig. 1".1, is ).# cm.alc!late the speed of so!nd in the t!be.

speed ' .........................................m s :1

[)]

(c) The wave in the t!be is a stationary wave. &xplain, by reference to the formation of a

stationary wave, what is meant by the speed calc!lated in (b)(ii).

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17 (a) *tate what is meant by(i) the frequency of a progressive wave,

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[](ii) the speed of a progressive wave..................................................................................................................................

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[1](b) %ne end of a long string is attached to an oscillator. The string passes over a frictionless

p!lley and is 5ept ta!t by means of a weight, as shown in Fig. 16.1.

Fig. 17.1

The fre7!ency of oscillation is varied and, at one val!e of fre7!ency, the wave formedon the string is as shown in Fig. 16.1.(i) &xplain why the wave is said to be a stationary wave.

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(ii) *tate what is meant by an antinode.

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(iii) %n Fig. 16.1, label the antinodes with the letter A.

[1]

(c) A weight of +.## / is h!ng from the string in (b) and the fre7!ency of oscillation is

adD!sted !ntil a stationary wave is formed on the string. The separation of the antinodeson the string is 16.G cm for a fre7!ency of 1- 89.

The speed v of waves on a string is given by the expression

where T is the tension in the string and m is its mass per !nit length.>etermine the mass per !nit length of the string.

mass per !nit length ' ........................................... 5g m :1 [-]

18 Two so!rces *1 and * of so!nd are sit!ated G# cm apart in air, as shown in Fig. 1G.1.


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Fig. 18.1

The fre7!ency of vibration can be varied. The two so!rces always vibrate in phase b!t have

different amplit!des of vibration.

A microphone 3 is sit!ated a distance 1## cm from * 1 along a line that is normal to *1*.

As the fre7!ency of *1 and * is grad!ally increased, the microphone 3 detects maxima and

minima of intensity of so!nd.

(a) *tate the two conditions that m!st be satisfied for the intensity of so!nd at 3 to be9ero.

1......................................................................................................................................

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[](b) The speed of so!nd in air is ))# m s :1.

The fre7!ency of the so!nd from *1 and * is increased. >etermine the n!mber of minima that will be detected at 3 as the fre7!ency is increased from 1.# 589 to +.# 589.

n!mber ' ................................................

[+]

1 (a) *tate what is meant by the diffraction of a wave.

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(b) A laser prod!ces a narrow beam of coherent light of wavelength ") nm. The beam is

incident normally on a diffraction grating, as shown in Fig. 1.1.

Fig. 1.1


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*pots of light are observed on a screen placed parallel to the grating. The distance

between the grating and the screen is 1"- cm.

The brightest spot is ;. The spots formed closest to ; and on each side of ; are 0

and E.

0 and E are separated by a distance of 6" cm.

alc!late the n!mber of lines per metre on the grating.

n!mber per metre ' .................................................

[+]

(c) The grating in (b) is now rotated abo!t an axis parallel to the incident laser beam, as

shown in Fig. 1..

Fig. 1.2

*tate what effect, if any, this rotation will have on the positions of the spots ;, 0 and E..........................................................................................................................................

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(d) 4n another experiment !sing the apparat!s in (b), a st!dent notices that the distances

0; and ;E, as shown in Fig. 1.1, are not e7!al.

*!ggest a reason for this difference.

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[1]

2! (a) *tate two feat!res of a stationary wave that disting!ish it from a progressive wave.

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[](b) A long t!be is open at one end. 4t is closed at the other end by means of a piston that

can be moved along the t!be, as shown in Fig. #.1.

Fig. 2!.1

A lo!dspea5er prod!cing so!nd of fre7!ency --# 89 is held near the open end of the t!be.

The piston is moved along the t!be and a lo!d so!nd is heard when the distance L between the piston and

the open end of the t!be is +- cm.

The speed of so!nd in the t!be is ))# m s :1.

(i) *how that the wavelength of the so!nd in the t!be is "# cm.

[1](ii) %n Fig. #.1, mar5 all the positions along the t!be of

1. the displacement nodes label these with the letter /C,2. the displacement antinodes label these with the letter AC.

[)](c) The fre7!ency of the so!nd prod!ced by the lo!dspea5er in (b) is grad!ally red!ced.

>etermine the lowest fre7!ency at which a lo!d so!nd will be prod!ced in the t!be of

length L ' +- cm.

fre7!ency ' .......................................... 89[)]

21 (a) A so!rce of so!nd has fre7!ency f . *o!nd of wavelength @ is prod!ced by the so!rce.

(i) *tate


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1. what is meant by the frequency of the so!rce,

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[1]2. the distance moved, in terms of @, by a wave front d!ring n oscillations of the

so!rce.

distance '..................................................

[1](ii) Ise yo!r answers in (i) to ded!ce an expression for the speed v of the wave in

terms of f and @.

[](b) The waveform of a so!nd wave prod!ced on the screen of a cathoderay oscilloscope

c.r.o.C is shown in Fig. 1.1.

Fig. 21.1

The timebase setting of the c.r.o. is .# ms cm :1.

(i) >etermine the fre7!ency of the so!nd wave.

fre7!ency ' ............................................89

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(ii) A second so!nd wave has the same fre7!ency as that calc!lated in (i). The amplit!de of the two waves

is the same b!t the phase difference between them is #$.

%n Fig. 1.1, draw the waveform of this second wave.

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