W5 Waves

Waves

• a disturbance that propogates
• depend on:
  • $x$: position
  • $t$: time
• $D$: displacement
• Snapshot graph
  • $D$ vs

Basic properties of periodic travelling wave

• $A$: amplitude (from zero to peak)
• $\lambda$: wavelength from (displacement from crest to crest, through to through or…)
• $T$ period (time from crest to crest, through to…)
• $v$ velocity (speed at which crest (etc.) moves)
• for some instant in time (snapshot):
  • $\boxed{y(x)=A\cos(\frac{2\pi}{\lambda}x)}$
• for some position in space (history):
  • $\boxed{y(t)=A\cos(\frac{2\pi}{T}t)}$
• 
• 

Sunisoidal Waves $v=f\lambda$

• phrase velocity ($v$)
  • $\boxed{v=f\lambda}
  • speed of a point of constant phase
  • NOT the same as $v_x$ for SHM
• $\boxed{D(x,t)=A\cos(2\pi(\frac{x}{\lambda}-\frac{t}{T}))=A\cos(kx-\omega t)}$
• $\boxed{T=\frac{2\pi}{\omega}}$
• $\boxed{\lambda=\frac{2\pi}{k}}$
• $\boxed{\omega=vk}$

Sound Waves

• changes in density
• Speed of sound $v\approx(331+0.60T)m/s, T\degree C$
• Displacement
  • $s(x,t)=s_m\cos(\frac{2\pi}{\lambda}x-\frac{2\pi}{T}t)$
  • $p()$
• Speed of sound
  • $\boxed{v=\sqrt{\frac{B}{\rho}}}$
    • $B$: bulk modulus (measure of how compressible)
    • $\rho$: mass density