Lecture 27

Readings

http://umdberg.pbworks.com/w/page/52298105/Wave%20speed

http://umdberg.pbworks.com/w/page/125131745/Workout%3A%20Wave%20speed

http://umdberg.pbworks.com/w/page/73086008/Superposition%20of%20waves%20in%201D%20%282013%29

Wave Speed

• Two speeds:

  

  • Speed of mass in medium

    • The speed of a single point on a string, or of a single mass for linked beads
    • It's in the $y$$y$-direction for transverse waves, so transverse to wave direction

  • Wave speed ( or wave velocity )

    • The "direction the crest of the wave is moving"
    • Here, this is the $+x$$+x$-direction

• For strings, find that the wave speed is:

  $$v=\sqrt{\frac{TensionintheString(T)}{MassDensityoftheString(\mu )}}$$

  • $\mu$$\mu$ = mass per unit length

    • NOT mass per unit volume

  

• So $v$$v$ increases if $T$$T$ increases or if $\mu$$\mu$ decreases, as seen in the activity

Superposition of Waves

• Superposition is a fancy wave of saying "they just add" or "the net result is the sum of each part"

• For waves:

  • If $f(x,t)$$f(x,t)$ is one wave, and $g(x,t)$$g(x,t)$ is another

    • Then if they happen to occur at the same spot in a string, the result will just be the sum:

      • $y(x,t)=f(x,t)+g(x,t)$$y(x,t) = f(x,t) + g(x,t)$

• Two opposite waves:

Clicker Questions