Waves & Sound — Cheat Sheet

WAVE FUNDAMENTALS

Amplitude (A)

max displacement from equilibrium

Wavelength (λ)

distance for one full cycle (m)

Period (T)

time for one full cycle (s)

Frequency (f)

cycles per second (Hz)

T = 1/f

period & frequency are reciprocals

v = fλ

wave speed (m/s)

Sound in air

≈ 340 m/s at 20°C

WAVE TYPES

Transverse: particle motion perpendicular to wave direction (light, string)

Longitudinal: particle motion parallel to wave direction (sound, compression)

SOUND IN MEDIA

Speed order: Solid > Liquid > Gas
Air ≈ 340 m/s · Water ≈ 1500 m/s · Steel ≈ 5000 m/s

SHM & PENDULUM

Restoring force: F = −kx
Force always directed back toward equilibrium

Pendulum T

T = 2π√(L/g)

L = length

g = 9.8 m/s²

Spring-mass T

T = 2π√(m/k)

Amplitude

Period is independent (small angles)

ENERGY IN SHM

Position	Speed	PE
Equilibrium	maximum	zero
Extreme (A)	zero	maximum

INTENSITY & DECIBELS

Inv sq law

I ∝ 1/r²

dB level

10 log(I / I&sub0;)

I&sub0;

10&sup-;¹² W/m² (threshold)

+10 dB = ×10 intensity
+3 dB ≈ doubled intensity

DOPPLER EFFECT

f_obs = f_s × (v ± v_obs) / (v ∓ v_s)

Observer → src

+ on top (higher f)

Observer ← src

− on top (lower f)

Source → obs

− on bottom (higher f)

Source ← obs

+ on bottom (lower f)

Doppler changes f only — NOT wave speed v

INTERFERENCE

Constructive

path diff = nλ (n = 0,1,2…)

Destructive

path diff = (n+½)λ

Waves in phase → amplitudes add
Waves out of phase → amplitudes cancel

STANDING WAVES

Node: zero displacement (always)
Antinode: maximum displacement

String / open

f_n = nv/(2L), n=1,2,3…

Closed pipe

f_n = nv/(4L), n=1,3,5…

Closed pipe: odd harmonics only
Open pipe & string: all harmonics

COMMON MISTAKES

T = 1/f (not T = f)
v = fλ: v fixed by medium, not source
Doppler changes f, NOT wave speed v
Pendulum T: independent of mass & amplitude
Constructive: not always doubled amplitude
Closed pipe: odd harmonics only

KEY NUMBERS

Sound (air)

≈ 340 m/s at 20°C

Gravity (g)

9.8 m/s²

I&sub0;

10&sup-;¹² W/m²