Interference of Sound Waves

Beginner Level

Split one sound into two paths and bring the parts together again. If they arrive together in step, the sound becomes loud. If a crest arrives with a matching trough, they cancel and the sound becomes very quiet.

Interference of Sound Waves

Overview

Sound interference can be demonstrated by sending one sound through two paths and recombining the waves at a receiver. The path difference determines whether the receiver detects a loud sound or cancellation; noise-cancelling headphones apply the same destructive-interference principle.

Learning Outcomes

• At the T-junction, sound energy divides between two paths r1 and r2 and recombines at receiver R.
• Equal paths make the waves arrive in phase, producing a loud sound by constructive interference.
• A path difference r2 - r1 = mλ also produces constructive interference.
• A path difference r2 - r1 = (m + 12)λ produces destructive interference and minimum sound.
• Blocking one path restores loudness, showing that the previous silence was caused by cancellation between two waves.
• Noise-cancelling headphones generate a wave with matching amplitude and opposite phase to reduce environmental noise.

Intermediate Level

Two-Path Sound Apparatus

A loudspeaker S sends sound into a tube at point P. A T-shaped junction divides the sound so that it travels along two routes to receiver R. The lower length r1 is fixed, while the upper U-shaped path r2 can be varied by sliding the tube.

Loud and Silent Conditions

If the paths are equal, Δr = 0 and the two portions arrive in phase, so R detects a loud sound. Increasing r2 can make the waves arrive 180° out of phase; then the receiver detects a sound minimum because the waves cancel.

Why Pinching One Path Is Evidence

At a destructive minimum, pinching the rubber part at Q stops the wave in one branch. The remaining wave reaches R alone, so a loud sound is heard again. This shows that the earlier silence came from two-wave cancellation rather than a stopped source.

Noise-Cancelling Headphones

A microphone senses unwanted environmental noise. The headphone electronics drive a loudspeaker to create a cancelling wave with approximately the same amplitude and the opposite phase. Their superposition reduces the resultant noise inside the ear cup.

Common Mistakes

• Silence in the two-path tube is caused by destructive interference, not by absence of sound energy from the source.
• Use the difference r2 - r1, not the sum r2 + r1, when testing the path condition.
• Equal path lengths produce constructive interference because the waves arrive in phase.
• An effective cancelling wave must have opposite phase and a suitable matching amplitude.

Short-Question Preparation

Sticky Notes

• At the T-junction, sound energy divides between two paths r1 and r2 and recombines at receiver R.
• Equal paths make the waves arrive in phase, producing a loud sound by constructive interference.
• A path difference r2 - r1 = mλ also produces constructive interference.
• A path difference r2 - r1 = (m + 12)λ produces destructive interference and minimum sound.
• Blocking one path restores loudness, showing that the previous silence was caused by cancellation between two waves.
• Noise-cancelling headphones generate a wave with matching amplitude and opposite phase to reduce environmental noise.

60-Second Revision

The sound splits into paths r1 and r2. Integral-wavelength path difference gives a loud maximum; an odd half-wavelength difference gives a minimum. Noise-cancelling headphones produce an opposite-phase wave to reduce unwanted sound.

Summary

Sound interference can be demonstrated by sending one sound through two paths and recombining the waves at a receiver. The path difference determines whether the receiver detects a loud sound or cancellation; noise-cancelling headphones apply the same destructive-interference principle.

Ask-the-Tutor Modes

• Explain the tube apparatus.
• Choose the loud or silent condition.
• Explain the pinching test.
• Explain noise cancellation.
• Test me with an MCQ.