IB Physics SL C: Wave Behaviour

Practise IB Physics SL wave behaviour through resonance, interference, diffraction, standing waves and Doppler effects, linking models to measurements.

Covered syllabus points

C.1 Simple harmonic motion C.2 Wave model C.3 Wave phenomena C.4 Standing waves and resonance C.5 Doppler effect

[Maximum number: 16]

This question is in two parts. Part 1 is about a thermistor circuit. Part 2 is about vibrations and waves.
Part 1 Thermistor circuit
The circuit shows a negative temperature coefficient (NTC) thermistor X and a $100 \mathrm{k} \Omega$ fixed resistor R connected across a battery.

Figure for Question C. Wave behaviour question 1 — IB Physics SL

The battery has an electromotive force (emf) of 12.0 V and negligible internal resistance.

(a)

Define simple harmonic motion (SHM).

[ 2 ]

(b)

D has mass $6.5 \times 10^{-3} \mathrm{~kg}$ and vibrates with amplitude 0.85 mm .

[ 4 ]

(i)

Calculate the maximum acceleration of D .

[ 2 ]

$\quad \omega=(2 \pi f=2 \pi \times 1250) 7854 \mathrm{rad} \mathrm{s}^{-1}$ ;

a_{0}=\left(-\omega^{2} x_{0}=-7854^{2} \times 0.85 \times 10^{-3}=\right)(-) 5.2 \times 10^{4} \mathrm{~ms}^{-2} ;

(ii)

Determine the total energy of D .

[ 2 ]

correct substitution into $E_{T}=\frac{1}{2} m \omega^{2} x_{0}{ }^{2}$ irrespective of powers of 10 ;

0.14 \text { to } 0.15 \mathrm{~J} ;

(c)

The sound waves from the loudspeaker travel in air with speed $330 \mathrm{~m} \mathrm{~s}^{-1}$ .

[ 4 ]

(i)

Calculate the wavelength of the sound waves.

[ 1 ]

(ii)

Describe the characteristics of sound waves in air.

[ 3 ]

(d)

A second loudspeaker S emits the same frequency as L but vibrates out of phase with L . The graph below shows the variation with time t of the displacement x of the waves emitted by S and L .

[ 6 ]

(i)

Deduce the relationship between the phase of L and the phase of S .

[ 3 ]

S leads L / idea that the phase of L is the phase of S minus an angle;
$\frac{1}{8}$ period $/ 1 \times 10^{-4} \mathrm{~s} / 0.1 \mathrm{~ms}$ ;
$\frac{\pi}{4} / 0.79 \mathrm{rad} / 45$ degrees;

(ii)

On the graph, sketch the variation with t of x for the wave formed by the superposition of the two waves. be marked.

[ 3 ]

Agreement at all zero displacements.
Maxima and minimum at correct times.
Constant amplitude of $1.60\ ext{mm}$ .

Figure for Answer to Question (ii) — IB Physics SL

[Maximum number: 11]

(a)

Outline what is meant by a travelling wave.

[ 2 ]

(b)

A loudspeaker emits sound of frequency 210 Hz into a pipe with one open and one closed end. The diagram shows a representation of the standing wave established in the pipe.

[ 5 ]

(i)

Outline how the standing wave is formed in the pipe.

[ 2 ]

(ii)

Determine the wavelength of the wave.

[ 1 ]

$\lambda=\lessdot \frac{4 L}{3}=\frac{4 \times 1.20}{3}=>1.6<\mathrm{m} \gg$

[1]

(iii)

Calculate the speed of sound in the pipe stating the answer to an appropriate number of significant figures.

[ 2 ]

$c=\ll \lambda f=1.60 \times 210 \Rightarrow \gg 336$ OR $340 \ll \mathrm{~m} \mathrm{~s}^{-1} \gg$
Any answer to 2 OR 3 s.f.

Marking guidance:

Allow ECF from incorrect wavelength in bii)

[2]

(c)

The solid line represents the standing wave at time t and the dotted line represents the standing wave at an instant later. The dot is the equilibrium position of a particle P in the pipe. The up arrow indicates displacements to the right and the down arrow displacements to the left.

On the diagram, draw

[ 2 ]

(i)

a dot to indicate the approximate position of P at time t,

[ 1 ]

(ii)

an arrow to indicate the velocity of P at time t.

[ 1 ]

(d)

The frequency of sound is reduced to 140 Hz . Explain why a standing wave will not be formed in the pipe.

[ 2 ]

[Maximum number: 3]

A group of students is investigating refraction in a semi-circular glass block.

Light from a ray box enters the curved side of the block. The light passes through the block and leaves, refracted, at P .

(a)

Outline how the students can ensure that the light is not deflected at the curved surface.

[ 1 ]

measure P to be at the centre of the flat edge/side so that incident rays are aimed at P /go through radial lines

OR

check that the incident angle is $0^{\circ}$ at every point of incidence

[1]

(b)

They plot a graph of the variation with the sine of $\theta_{i}$ of the sine of $\theta_{r}$ .
They add uncertainty bars for $\sin \theta_{r}$ for the first and last data point and draw the best-fit line.

[ 2 ]

(i)

Determine the value of the refractive index of the glass with its absolute uncertainty.

[ 2 ]

States gradient gives the value of the refractive index

OR

n=1.5 $n=1.5 \pm 0.2$

MP1 can be shown as an equation.

Candidates may calculate the uncertainty by using the gradient of the line found in cii) or finding the average of the max and min lines of best fit.

Look for working leading to $0.1 \leq \Delta n \leq 0.2$ .

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Covered syllabus points

C. Wave behaviour question 1

Question (a)

Question (b)

Question (i)

Question (ii)

Question (c)

Question (i)

Question (ii)

Question (d)

Question (i)

Question (ii)

C. Wave behaviour question 2

Question (a)

Question (b)

Question (i)

Question (ii)

Question (iii)

Question (c)

Question (i)

Question (ii)

Question (d)

C. Wave behaviour question 3

Question (a)

Question (b)

Question (i)