IB Physics HL Theme C: Wave behaviour questions

Exam-style multiple choice and written questions with full markschemes. Check multiple choice answers straight away, or type, photograph or draw a written answer and get it marked.

Type

Multiple choice Written

Difficulty

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Question 1

Multiple choiceHard1 mark

An oscillator has a period of $2.0\ \text{s}$ Four proposed graphs show its acceleration $a$ against displacement $x$ measured from equilibrium. Which trace is consistent with the oscillator undergoing simple harmonic motion?

Show answer and explanation

Answer: A. For simple harmonic motion, the graph of $a$ against $x$ is a straight line through the origin with gradient $-\omega^2$ From $T=2.0\ \text{s}$ $\omega=2\pi/T=\pi\ \text{rad s}^{-1}$ so the required gradient is $-\pi^2\approx-9.87\ \text{s}^{-2}$ Trace P has this negative gradient and passes through the origin.
B: uses a negative gradient through the origin, but its magnitude is about $3.14\ \text{s}^{-2}$ confusing $\omega$ with $\omega^2$
C: has the required gradient but does not pass through the origin, so acceleration is not proportional to displacement.
D: has a positive gradient, so acceleration is in the direction of displacement rather than towards equilibrium.
Remember: SHM requires acceleration to be proportional to displacement and opposite in direction.

Question 2

Paper 2Hard10 marks

A cord and a spring each carry a sinusoidal travelling disturbance along the equilibrium $x$ -axis. Figure 1 shows the displacement of particles from equilibrium at $t=0$ and $t=0.20\ \mathrm{s}$ plotted against each particle’s equilibrium coordinate $x$ In the upper panel, $y$ is the cord-particle displacement perpendicular to $x$ with positive $y$ upwards. In the lower panel, $u$ is the spring-particle displacement along $x$ with positive $u$ in the $+x$ direction. Each disturbance retains its profile as it travels.

(a)

Determine the direction of propagation and the speed of the disturbance on the cord.

[2]

(b)

State the wavelength of the disturbance on the cord.

[1]

(c)

At $x=0.20\ \mathrm{m}$ determine the instantaneous velocity of the cord particle at $t=0.20\ \mathrm{s}$ Give your answer with its direction.

[4]

(d)

The spring disturbance is now launched in the opposite direction, with its speed and wavelength unchanged. Describe how its profile at $t=0.20\ \mathrm{s}$ is displaced relative to its profile at $t=0$ State whether the disturbance is still longitudinal, and explain your answer.

[3]

Question 3

Paper 2Hard10 marks

In a laboratory, a laser illuminates both slits of a double-slit plate at normal incidence. The separation of adjacent bright fringes is measured on a screen parallel to the plate. A reference laser has wavelength $600\ \mathrm{nm}$ With the original plate and a screen distance of $1.20\ \mathrm{m}$ the measured fringe separation is $3.00\ \mathrm{mm}$

(a)

Show that the slit separation of the original plate is approximately $0.240\ \mathrm{mm}$

[2]

(b)

The screen is moved to a distance of $1.80\ \mathrm{m}$ with the original plate and reference laser unchanged. Determine the fringe separation.

[1]

(c)

A replacement plate is used with the reference laser and the screen at $1.80\ \mathrm{m}$ The measured fringe separation is $3.00\ \mathrm{mm}$ Determine the slit separation of the replacement plate.

[1]

(d)

The replacement plate is used with an unknown laser wavelength. The screen is at $1.20\ \mathrm{m}$ and the fringe separation is $2.40\ \mathrm{mm}$ Determine the wavelength of this laser.

[2]

(e)

In a further run, an unknown laser gives a fringe separation of $3.00\ \mathrm{mm}$ with the screen at $1.20\ \mathrm{m}$ but the identity of the slit plate used was not recorded. A technician claims that the laser wavelength is the same as that of the reference laser. Determine whether this claim is justified, supporting your answer quantitatively.

[4]

Question 4

Paper 2Hard10 marks

A sound emitter moves uniformly through still air. At one instant, the distance between adjacent wavefronts is 0.646 m ahead of the emitter and 0.714 m behind it. The speed of sound in the air is 340 m s⁻¹. In a second arrangement, the emitter is stationary and a detector moves towards it at the speed found in (a). The emitter has the same frequency in both arrangements.

(a)

Determine the emitted frequency and the speed of the emitter. Show your reasoning.

[4]

(b)

Sketch wavefront diagrams for (i) the sound emitter moving towards a stationary detector and (ii) a stationary emitter with the detector moving towards it. Indicate the directions of motion and the relative spacing of the wavefronts.

[2]

(c)

Calculate the frequency detected in each sound arrangement. Give your answers to three significant figures.

[2]

(d)

A light beacon moves towards an observer. State how the detected frequency and wavelength compare with those emitted, and state one relevant difference between light waves and sound waves.

[2]

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