Explain why two loudspeakers connected to the same signal generator and placed a small distance apart produce regions of loudness and silence when a listener walks slowly along a line parallel to and several metres from the loudspeakers.
Written & reviewed by James Millett — Biology (Imperial College London), PGCE Science (University of Cambridge).
Two loudspeakers are connected to the same signal generator so that they emit sound waves of identical frequency and amplitude in phase with each other.
Model answer (4 marks)
The two loudspeakers are coherent sources, emitting waves of the same frequency and with a constant (zero) phase difference.
At any point along the line the path difference between the two waves varies.
Where the path difference equals an integer multiple of the wavelength (nλ), the waves arrive in phase and interfere constructively, giving a region of maximum loudness.
Where the path difference equals an odd multiple of half a wavelength ((n+½)λ), the waves arrive out of phase and interfere destructively, giving a region of minimum loudness (silence).
At any point along the line the path difference between the two waves varies.
Where the path difference equals an integer multiple of the wavelength (nλ), the waves arrive in phase and interfere constructively, giving a region of maximum loudness.
Where the path difference equals an odd multiple of half a wavelength ((n+½)λ), the waves arrive out of phase and interfere destructively, giving a region of minimum loudness (silence).
Examiner tips
- Use the term ‘coherent sources’ to show understanding of phase relationship.
- Explain how the path difference changes with position and link it to constructive/destructive interference.
- Show the two conditions (nλ and (n+½)λ) explicitly.
- Keep the answer concise – 4 marks can be earned with 4 short sentences.
Mark scheme (4 marks)
- The two loudspeakers act as coherent sources, emitting waves of the same frequency and with a constant (zero) phase difference.
- At different positions along the line, the path difference from each speaker to the listener's ear varies.
- Where the path difference is a whole number of wavelengths (nλ), the waves arrive in phase and interfere constructively, producing a region of maximum loudness.
- Where the path difference is an odd number of half-wavelengths ((n + ½)λ), the waves arrive in antiphase and interfere destructively, producing a region of silence (or minimum loudness).
Related
- All IB DP Physics Higher Level (2023 syllabus) revision notes →
- How to answer a "Explain" question →
- Decode the mark scheme abbreviations →
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