IB Physics SL 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

Easy Medium Hard

Question 1

Paper 2Hard10 marks

A small mass attached to a vertical spring oscillates in simple harmonic motion between upper turning point U and lower turning point L, passing through equilibrium position O. The spring remains stretched throughout the motion. Consider the mass, spring and Earth as the system. Air resistance and other resistive forces are negligible. The mass is released from rest at U. Its mechanical energy consists of kinetic, gravitational potential and elastic potential energy.

(a)

As the mass moves from U to L, state how its gravitational potential energy and elastic potential energy change.

[2]

(b)

At which position, U, O or L, is the kinetic energy greatest?

[1]

(c)

Compare the total potential energy of the system at U and L. Explain your answer with reference to the gravitational and elastic potential energies.

[3]

(d)

A student says: “The gravitational potential energy is lower at L than at U, so mechanical energy has been lost during the motion from U to L.” Evaluate this statement by describing the energy changes over U→O→L→U.

[4]

Question 2

Paper 2Medium8 marks

A laboratory compares a piezoelectric transducer producing sound in water with an antenna emitting electromagnetic radiation into a vacuum. Both waves have a frequency of $2.00\times10^6\ \mathrm{Hz}$

The speed of sound in water is $1.50\times10^3\ \mathrm{m\,s^{-1}}$ The speed of electromagnetic waves in a vacuum is $3.00\times10^8\ \mathrm{m\,s^{-1}}$

(a)

Calculate the wavelength of the sound wave in water.

[2]

(b)

Calculate the wavelength of the electromagnetic wave and, using the approximate wavelength orders of magnitude in the data booklet, identify its region of the electromagnetic spectrum.

[3]

(c)

Using your answers to (a) and (b), determine the ratio $\lambda_{\text{electromagnetic}}/\lambda_{\text{sound}}$

[1]

(d)

The two signals are directed across an evacuated region towards detectors. State which signal can cross the region and explain your answer with reference to the nature of each wave.

[2]

Question 3

Paper 2Medium9 marks

Two transverse pulses travel in opposite directions along the same string. At one instant, they overlap. The individual displacements of the pulses at three positions on the string are shown below. Displacements are measured from the equilibrium position; upward displacements are positive.

Position, x / cm	Pulse A displacement / cm	Pulse B displacement / cm
1.0	+2.0	+1.0
2.0	+4.0	−4.0
3.0	+2.0	−1.0

(a)

State the displacement of pulse A at x = 2.0 cm.

[1]

(b)

Determine the displacement of the string at each of the three positions.

[3]

(c)

Identify whether the interference at x = 3.0 cm is constructive or destructive. Explain your answer using the data.

[2]

(d)

At x = 2.0 cm, the resultant displacement is zero. Explain why this does not mean that the pulses have been destroyed, and describe their motion and shape once they have passed through one another completely.

[3]

Question 4

Paper 2Medium9 marks

A panel in a vibrating screen is driven by a motor. Large oscillations help the screen separate particles, but excessive vibration can loosen joints in the supporting machine. The panel has a natural frequency of $4.0\ \mathrm{Hz}$

The following amplitudes were measured after the oscillations had reached a steady state. Treat the driving frequency at which the greatest amplitude is recorded as the resonant frequency for these measurements.

Driving frequency / Hz	Amplitude with weak damping / mm	Amplitude with strong damping / mm
2.0	2	3
2.5	3	5
3.0	6	8
3.5	10	7
4.0	9	5
4.5	5	3
5.0	2	2

(a)

State what is meant by the natural frequency of the panel.

[1]

(b)

For each damping condition, determine the driving frequency at which the greatest amplitude was recorded.

[2]

(c)

Using the data, compare the effects of increasing the damping on the greatest amplitude and on the frequency at which it occurs.

[2]

(d)

The screen is driven at $3.5\ \mathrm{Hz}$ Select the damping condition that would produce more effective particle separation, and explain why the panel has a large response at this driving frequency.

[2]

(e)

Explain why engineers might nevertheless choose strong damping, even if this reduces the screen’s effectiveness.

[2]

Question 5

Paper 2Easy9 marks

A sound source emits a steady tone into still air. Its emitted frequency is $f_s$ in both situations shown in Figure 1. The figure shows successive wavefronts along the line of motion at one instant. In A, the source is fixed and O moves as indicated. In B, the source moves as indicated while O₁ and O₂ are stationary. The diagrams are schematic; compare only the separations of adjacent wavefronts.

(a)

Describe the spacing of the wavefronts in A and state whether motion of O changes their spacing in the air.

[2]

(b)

Explain whether the frequency heard by O is higher or lower than $f_s$

[2]

(c)

In B, state the direction in which the source moves and compare the wavefront spacing ahead of and behind it.

[3]

(d)

State whether O₁ hears a frequency higher or lower than $f_s$

[1]

(e)

State whether O₂ hears a frequency higher or lower than $f_s$

[1]

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