Waves & Sound
Wave properties, superposition, interference, standing waves, sound, and the Doppler effect.
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Wave Basics
- A wave transfers energy without net transfer of matter.
- v = fλ; period T = 1/f.
- Transverse vs longitudinal; mechanical vs electromagnetic.
v = fλ
T = 1/f
y(x,t) = A sin(kx − ωt + φ)
Interference & Superposition
- When two waves meet, displacements add (principle of superposition).
- Constructive: path difference = mλ; destructive: (m+½)λ.
- Beats: |f₁ − f₂| when two close frequencies interfere.
Δ = mλ (constructive)
Δ = (m+½)λ (destructive)
f_beat = |f₁ − f₂|
Standing Waves & Doppler
- Standing wave on string (fixed ends): λₙ = 2L/n, fₙ = n v/(2L).
- Doppler (source moving): f′ = f · v/(v ± v_s).
- Nodes are points of zero amplitude; antinodes are maximum amplitude.
λₙ = 2L/n
f′ = f v/(v ± v_s)
Full topic quiz — 100 MCQs
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Quick practice (sample):
Quick quiz
1. Beat frequency for 440 Hz and 444 Hz is:
2. For a string fixed at both ends, the fundamental wavelength is:
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