Course:PHYS341/2018/Calendar/Lecture04

Phys341 Lecture 04: Summary and web references

2018.01.10

Textbook: Section 4.1-4.4

Slide List

Lecture 4: Longitudinal Waves

1. Longitudinal waves https://www.youtube.com/watch?v=ubRlaCCQfDk
2. Acoustic Waves
3. Pressure disturbances in a fluid or solid propagate outward from the source as acoustic waves.
   • There are also accompanying density variations but we usually talk about pressure fluctuations as these can be measured more directly (with a microphone). For the simulations it is easy to see the density variations.
   • For a gas like air, pressure is proportional to density.
   • For sound in air, the pressure variations are generally tiny compared to the static absolute air pressure (i.e. that which is reported by weather stations).
   • Acoustic pressure refers to the relatively tiny fluctuations in the much larger static air pressure. An amplitude of a billionth of the static pressure can still be heard at audio frequencies.
4. Gases
   • At the macroscopic level, gases have
   • Pressure
   • Density
   • Temperature
   • When a gas is squeezed (think of a bicycle pump)
   • You apply a force, and gas reacts with an opposite force (Newton III), pressure rises
   • You squeeze the same mass into a smaller volume, so the density goes up
   • You do mechanical work on the system, so it heats up, temperature rises
5. Kinetic theory https://en.wikipedia.org/wiki/Kinetic_theory_of_gases (see first animated gif)
   • The way gases behave can be understood entirely in terms of their physical composition.
   • Large numbers of very small particles (i.e. molecules, atoms) moving in random directions. This is thermal motion.
   • Colliding with each other and the walls of their container.
   • Air molecules (e.g. two atoms of nitrogen bound together) at room temperature have a mean speed of 500 m/s and travel an average of 0.1 μm before collision with another.
6. Microscopic view of a sound wave http://www.acs.psu.edu/drussell/Demos/waves/wavemotion.html
7. Travelling Longitudinal wave simulation
8. Adding left and right waves
9. A complication: two kinds of nodes
   • The biggest density (pressure) changes occur where the displacements are minimum
   • The extreme case is when the wave hits a solid wall: the density varies maximally, but the particles cannot move.
   • So, density (pressure) antinodes are displacement nodes.
   • Likewise, density (pressure) nodes are displacement antinodes.
10. A complication: two kinds of nodes see http://hyperphysics.phy-astr.gsu.edu/hbase/Waves/standw.html
11. Standing waves in pipes
    • In principle an infinite series of ever-increasing frequency and ever-decreasing wavelength
    • Which wavelengths will fit depends on whether the ends are open or closed
    • If the end is closed there is a velocity node (because the air cannot move against a solid wall) and a pressure antinode (because the air can squash up against the wall)
    • If the end is open there is a pressure node (because the air can move freely in and out) and a velocity antinode (for the same reason)
    • By imposing these conditions, we get a set of allowed frequencies for standing waves in the pipe