IB Physics HL Theme C: Wave behaviour questions

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Question 1

Multiple choiceMedium1 mark

A source produces periodic waves in medium X with wavelength $\lambda$ period $T$ and speed $v$ The source is adjusted to produce waves with period $T/2$ in medium Y, where their speed is $3v$ What is the wavelength of the waves in medium Y?

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Answer: B. Since $v=f\lambda$ and $f=1/T$ wavelength is $\lambda=vT$ The wavelength in medium Y is $(3v)(T/2)=3vT/2=3\lambda/2$

A: applies the period change but leaves the wave speed unchanged.
C: applies the speed change but leaves the period unchanged.
D: uses $2T$ instead of $T/2$ then applies the speed factor of 3.

Remember: wavelength is the product of wave speed and period.

Question 2

Multiple choiceMedium1 mark

A travelling wave P has frequency $f$ and wavelength $\lambda$ A second travelling wave Q has the same speed as P and a frequency of $2f$ In Q, particles oscillate parallel to the direction of travel. Which description of Q is correct?

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Answer: C. Q is longitudinal because its particles oscillate parallel to the direction of travel. Since the two waves have the same speed, $v=f\lambda=(2f)\lambda_Q$ so $\lambda_Q=\frac{\lambda}{2}$

A: reverses the wave classification and treats wavelength as directly proportional to frequency.
B: finds the wavelength correctly but labels parallel oscillations as transverse.
D: identifies the wave correctly but uses a direct rather than inverse frequency–wavelength relationship.

Remember: at fixed wave speed, frequency and wavelength are inversely proportional.

Question 3

Multiple choiceMedium1 mark

A monochromatic beam illuminates two identical slits, each of width $a$ whose centres are separated by $d$ The ratio $d/a$ is an integer greater than 1. Which order of the two-slit interference pattern is absent because it coincides with the first minimum of the single-slit diffraction envelope?

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Answer: B. At the first single-slit minimum, $a\sin\theta=\lambda$ A missing interference maximum occurs at the same angle, where $d\sin\theta=n\lambda$ Equating the angles gives $n=d/a$

A: reverses the ratio of slit width to centre separation.
C: uses the first diffraction-minimum index as the interference order without matching the angles.
D: uses twice the first-minimum condition, introducing an extra factor of 2.

Remember: an interference order is missing when its maximum coincides with a diffraction minimum.

Question 4

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?

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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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