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Formula Sheets / Physics

Chapter 17

Waves and Sound

Revise with flashcards Download this chapter (PDF) All Physics formulas (PDF)

Wave motion Waves on a string and standing waves Sound, organ pipes and beats Doppler effect

Wave motion

$y = A sin (k x - ω t),$ $v = f λ = \frac{ω}{k},$ $k = \frac{2 π}{λ}$
Phase difference
$Δ ϕ = \frac{2 π}{λ} Δ x$
Intensity
$I = 2 π^{2} f^{2} A^{2} ρ v;$ $I \propto \frac{1}{r ^{2}}$ (point source)
Sound level
$β = 10 lo g_{10} \frac{I}{I _{0}}$ dB

Waves on a string and standing waves

Speed
$v = \frac{T}{μ}$
String fixed at both ends
$f_{n} = \frac{n v}{2 L},$ $n = 1, 2, 3, \dots$
Standing wave
$y = 2 A sin k x cos ω t;$ node to node $= \frac{λ}{2}$

Sound, organ pipes and beats

Speed of sound
$v = \frac{γ P}{ρ} = \frac{γ R T}{M};$ $v_{solid} = \frac{Y}{ρ}$
Open pipe
$f_{n} = \frac{n v}{2 L},$ $n = 1, 2, 3, \dots$
Closed pipe
$f_{n} = \frac{n v}{4 L},$ $n = 1, 3, 5, \dots$ (odd harmonics only)
End correction
$L \to L + 0.6 r$ (closed) $,$ $L + 1.2 r$ (open)
Beats
$f_{beat} = ∣ f_{1} - f_{2} ∣$
Resonance tube
$v = 2 f (l_{2} - l_{1})$

Doppler effect

$f^{'} = f \frac{v \pm v _{o}}{v \mp v _{s}}$
Upper signs when observer and source move towards each other.

Oscillations Electrostatics