Interference occurs when waves interact due to differences in path lengths traveled. Constructive interference happens when path differences are integer multiples of the wavelength, while destructive interference occurs when path differences are half-integer multiples. Concert halls and theaters aim to reduce destructive interference through strategic wall and ceiling design to absorb reflected sound waves and prevent interference. Noise-cancelling headphones also use destructive interference by generating out-of-phase sound waves to cancel out surrounding noise.

2. SUMMARY
• Constructive and destructive interference
• Spherical waves oscillate in time and space
• s(r,t)= sm(r)cos(kr-wt+ϕ)

3. CONSTRUCTIVE
• Amplitudes add
• When the wavelengths are a multiple of an integer they are in phase
• Δd=pλ where p is an interger

4. DESTRUCTIVE
• When sources are out of phase destructive interference occurs
• Path difference is half of an interger multiple.
• Δd=(n+1/2)λ where n is an interger

5. APPLICATION
Concerts and Theatres
Must be designed in order to reduce destructive interference.
Question:
What are some ways that you could reduce the destructive interference?

6. ANSWER
Some examples include:
Design of walls and ceilings
Why? If the material used can absorb the sound then less sound will be
reflected. This means less opportunity for destructive interference.

7. APPLICATION
Question:
How do noise cancelling headphones work?
Answer:
Through computer programming the headphones create a noise that is half
a phase out of the surrounding noise resulting in destructive
interference.