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.