Reading assignment: 18.4-18.7
The boundary conditions for waves on a string with two fixed ends
leads to a fundamental mode which looks like half a sine wave, oscillating up
and down. But what happens if one end is fixed and the other is free to move? What
would the fundamental mode look like for that case?
Frozen in time it looks like a quarter of a sine wave, just like the first harmonic open/closed pipe picture in Fig 18.13b (8th edition)
In the context of waves, what is "beating" and why does it occur? Explain in
your own words, as if to someone who is not familiar with physics.Beating is a periodic increase/decrease in amplitude of the wave, that occurs (for example) when two instruments that are slightly out of tune play the same note. It happens because the slight change in wavelength causes the maxima/minima to not occur quite together--they only occur together once every hundred (or so) times. When the maxima do occur together, the volume is increased.
Give an example of resonance from everyday life.
My favorite example is the trumpet. When the proper frequency is "buzzed", the entire air column inside the instrument starts oscillating resonantly, producing a very loud and bright sound.