IBDP Physics- C.2 Wave model- IB Style Questions For HL Paper 2 -FA 2025
Question
(i) Determine the wavelength and the period of the sound wave.
(ii) Hence calculate the speed of the sound wave.
(i) Describe the Doppler effect.
(ii) A car travels at a constant speed \(v\) between two stationary sound sources, as shown. One source emits sound at 440 Hz and the other at 540 Hz. The driver hears both sounds at the same frequency. The speed of sound is 340 m s\(^{-1}\).
(iii) Light received from a distant galaxy shows a peak wavelength of 659.0 nm. This peak corresponds to a hydrogen atomic transition that has a wavelength of 656.1 nm when measured in a laboratory on Earth.
Determine the velocity of the galaxy relative to Earth.
Most-appropriate topic codes (IB Physics 2025):
• C.5: Doppler effect — parts (c)(i), (c)(ii), (c)(iii)
▶️ Answer/Explanation
(a)
Any two of the following:
• Sound waves are longitudinal, whereas light waves are transverse.
• Sound waves require a material medium; light waves can propagate through a vacuum.
• Sound waves are mechanical; light waves are electromagnetic.
Answer: Any two valid differences.
(b)(i)
From Graph 1, the wavelength is \( \lambda \approx 0.68\,\text{m} \).
From Graph 2, the period is \( T = 0.002\,\text{s} \).
(b)(ii)
\( v = \dfrac{\lambda}{T} = \dfrac{0.68}{0.002} = 340\,\text{m\,s}^{-1} \).
(c)(i)
The Doppler effect is the apparent change in frequency or wavelength of a wave due to relative motion between the source and the observer.
(c)(ii)
For the 440 Hz source (car moving away): \( f_1 = 440 \dfrac{340 – v}{340} \).
For the 540 Hz source (car moving towards): \( f_2 = 540 \dfrac{340 + v}{340} \).
Since \( f_1 = f_2 \):
\( 440(340 – v) = 540(340 + v) \).
Solving gives \( v \approx 35\,\text{m\,s}^{-1} \).
(c)(iii)
\( \Delta \lambda = 659.0 – 656.1 = 2.9\,\text{nm} \).
\( \dfrac{\Delta \lambda}{\lambda} \approx \dfrac{v}{c} \).
\( v = 3.0 \times 10^8 \times \dfrac{2.9}{656.1} \approx 1.3 \times 10^6\,\text{m\,s}^{-1} \).
The increase in wavelength indicates the galaxy is moving away from Earth.