12.3 Properties of Waves

- A wave is a rhythmic disturbance that caarries energy through matter or space at a constant speed.

- Mechanical waves such as water and soundd waves require a medium to travel through.

- Electromagnetic waves such as light and radio waves can travel through the vacuum of space.

- A pulse wave is a single bump or disturbbance that travels through a medium.

- A periodic wave is a train of pulses prooduced by a source with periodic motion.

- Periodic waves of all kinds have sinusoiidal waveforms, that is their wave pattern can be described graphically by a sine wave curve.

y = sin x

- Transverse waves oscillate perpendicularr to the direction of wave motion.

- Longitudinal waves oscillate parallel too the direction of wave motion.

- A sound wave is an example of a longituddinal wave.

- Earthquakes and water waves are two exammples of waves that are both transverse and longitudinal.

- There are three quantities useful in desscribing periodic waves:

1. ) wave speed v
   
   
2. ) wavelength λ
   
   
3. ) frequency f

v = f λ

- The Amplitude is the maximum displacemennt from the equilibrium position.

-Through conservation of energy, an equatiion involving position can be developed.

E_total = KE + PE

1/2 kA² = 1/2 mv² + 1/2 kx²

- At the equilibrium position, the object expresses it's greatest velocity and no acceleration.

v_max = 2πf A

KE_max = 1/2 mv² = m 2π²f ² A² = PE_max

- At an amplitude, the velocity of an objeect is zero, but its acceleration is at its maximum.

a_max = 4π²f ² A

PE_max = 1/2 kA² = KE_max