IB Physics HL 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.

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Question 1

Paper 2Easy9 marks

A string on a musical instrument is fixed at both ends and vibrates in the mode shown in Figure 1.

(a)

State the number of displacement nodes and the number of antinodes shown. Count the fixed ends as nodes.

[2]

(b)

The string has length $0.600\ \mathrm{m}$ and the wave speed on it is $120\ \mathrm{m\,s^{-1}}$ For the mode shown, calculate the wavelength and frequency. Give both answers to 3 significant figures.

[3]

(c)

Compare the oscillation amplitudes at A and B, and state their phase difference.

[2]

(d)

Sound travels at $340\ \mathrm{m\,s^{-1}}$ in a pipe of length $0.600\ \mathrm{m}$ The pipe is closed at one end and open at the other. Calculate the wavelength and frequency of the third harmonic. Ignore end correction.

[2]

Question 2

Multiple choiceMedium1 mark

Two sinusoidal waves, each of amplitude $a$ and wavelength $\lambda$ travel in opposite directions along a string and form a standing wave. There is a displacement node at $x=0$ Points $P$ and $Q$ are at $x=\lambda/12$ and $x=\lambda/3$ respectively. What is the ratio of the oscillation amplitude at $P$ to that at $Q$ and what is the phase difference between their oscillations?

Show answer and explanation

Answer: C. For two equal waves forming a standing wave with a node at $x=0$ the amplitude at position $x$ is $2a|\sin(2\pi x/\lambda)|$ Thus $A_P=a$ and $A_Q=\sqrt{3}a$ giving $A_P/A_Q=1/\sqrt{3}$ Both points lie between the same pair of adjacent nodes, so their oscillations are in phase and their phase difference is $0$

A: reverses the requested amplitude ratio.
B: finds the ratio correctly but treats points in the same segment between nodes as oscillating in antiphase.
D: assumes amplitude is proportional to distance from the node, giving $x_P/x_Q=1/4$

Remember: points in the same segment between adjacent nodes oscillate in phase.

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