IB Physics SL C.4 Standing waves and resonance 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

Multiple choiceEasy1 mark

A string supports a standing wave. Points P and Q are antinodes immediately on opposite sides of the same displacement node. What is the phase difference between the oscillations of P and Q, in radians?

Show answer and explanation

Answer: C. Adjacent antinodes separated by a displacement node oscillate in antiphase: when one is at maximum positive displacement, the other is at maximum negative displacement. This is a half-cycle separation, so $\Delta\phi = 2\pi(1/2) = \pi\ \text{rad}$ A: treats the two points as oscillating in phase. B: assigns a quarter-cycle separation instead of opposite-phase motion. D: assigns a three-quarter-cycle separation instead of a half-cycle. Remember: antinodes in neighbouring segments separated by a node oscillate in antiphase.

Question 2

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]

The best questions are still waiting

Unlock every question in this topic, then type, photograph or draw your answer and have it marked against the markscheme. Find out where you are dropping marks.

Unlock all questions Compare Student and Student Plus