'Model the effect of different materials on the reflection and absorption of sound'

• i) The American Standards version (using a reflectance tube) can be adapted for experimental investigations. PVC water or sewage pipe is fine for this purpose, and good fitting caps are available cheaply from a plumbers' suppliers. The material to be tested should be cut to fit neatly inside the pipe. A slot in the pipe allows you to scan one or preferably two microphones along the pipe. (Ideally seal the slit around the mics.) Mics are connected to CRO. Speaker shouldn't touch pipe to avoid mechanical effects.
  

  Relating these to the reflection and transmission coefficients is relatively simple algebra. The material has a reflection coefficient that is less than one, so the wave in the tube is the sum of a wave to the right and a smaller wave to the left. This can also be written as the superposition (sum) of a standing wave and a wave to the right. At the node of the standing wave, the amplitude (the minimum amplitude measured in the tube) equals the amplitude of the travelling wave, i.e. the difference between the incident and reflected. At the antinode of the standing wave, the amplitude is the sum of the incident and reflected.
  Another tube cap, with a hole cut slightly smaller than the ID of the tube, could be used for a rough-and- ready measurement of transmission with a microphone just outside. This requires baffles and is less exact, but you could use the same gear. Perhaps point it out through a window to minimise reflections onto your external mic, and then the wall is part of your baffle. Most sound absorbant materials (like acoustic wool, carpet, fibreglass batts) absorb much more in the kHz range than at low frequencies.
  'Modelling the effects of different materials'. Perhaps this just means that one calculates what different reflection and transmission coefficients would do to experiments like those above. The effects in practical geometries, such as a room, involve many reflections and are thus rather involved to model directly. Some acousticians are now doing that with huge ray-tracing calculations, but it is rather time consuming for a high school project. Alternatively, one could go straight to the reverberation time and Sabine's formula for it. Perhaps we should wait for clarification on what is meant here

• ii) Free field measurements are complicated indoors by the difficulty of obtaining a free field. You can set up a nearly plane wave reflecting at a wall by having the source >> lamda away, but don't make it too far away or else reflections from other surfaces are important. Stay either very near or very far from the floor. Then the reflecting material can be fixed to the wall.

• i) The time of flight is more direct. Two channel CRO, two mics and compare phase. (This can be done at the same time as the p ~ 1/r experiment. Careful about reflections.
  You can use one mic and use the reflection: using impulse source. This is more easily done with a sound card or storage CRO, but can be done on a single trace CRO using careful triggering. Set the trigger to normal and adjust the trigger level so that it triggers on the first sound and not on echos. Watch out for multiple reflections (and/or set the CRO trace to catch only the first). The further your reflector, the slower the trace and so the easier it is to see the reflection on a non-storage oscilloscope.

• ii) Time of flight in a waveguide. Here is a very low tech measurement, accurate to a few percent. Use a long hose (say 20 m, larger ID reduces the attenuation due to wall losses. Garden hose is a bit too narrow: I use plastic irrigation hose 19 mm diameter). Tap an open end with the flat of the hand at one end and listen to the sound of the tap and of the reflection. Listen carefully to the two sounds (slap thump - in the echo the high frequency components are more attenuated than the low). Pretend that these are the first two beats in a simple rhythm (most people have a reasonably accurate sense of rhythm) Count multiples of the interval for 10 or 20 periods. Remember to count from zero and that it's a round trip. Close the far end of the pipe with a cork so you don't hear the first reflection. This is will easily give a value within several percent of the standard value.

• iii) Standing waves in a cylindrical tube are less direct but give greater precision. Because of end effects on open tubes, the change in length of tube required for one extra half wavelength is a good way to get l. (i.e. go up one harmonic, then adjust the length to get the same frequency). The length of the end effect is only weakly dependent on frequency (to a good approximation, an unbaffled tube's effective end is 0.6 times the radius beyond its real end).
  A slide whistle (swannee whistle) is a cylindrical resonator with a moveable stop and an inbuilt control oscillator. Blow a note with the plug nearly all the way in. Then find a position with the slide further out and that gives the same note. This is one (or just possibly two) halfwavelengths. Most people have a sense of pitch accurate to better than 1% in frequency. Slide whistles cost only a few $ but the sound of a classroom of students using them.....
  A trombone has a long cylindrical, continuously adjustable section and can do the same thing. Because the slide is easily damaged, there are lots of unplayable trombones around that will still serve for this experiment. The school band or local junk shop may have one. A mute may be worth the price.

iv) For approximate results, one can use a narrow cylindrical tube and neglect end effects. A cylindrical dijeridu is readily made from 1-2 m of plastic conduit or plumbing pipe (smooth the end to be blown). A flute is approximately cylindrical. These can be used as the 'contextual' introduction to the exercise. (Our site on the acoustics of music has introductory material on a range of topics.)

Waves in slinky springs, water waves, ropes, strings. Displacement-time graphs

To reduce friction, suspend a slinky spring from a rod or from the ceiling by many threads of equal length threads (the longer the better for transverse waves in a nearly linear medium). This is a good way to allow a wave under low tension - and therefore speed: slow enough to see in detail. This method also shows reflection at a free end (or at least a big change in impedance) more easily than most media. The tension is controled by a thread at the end (~ free end for transverse wave), or by holding it firmly in a hand (~ fixed end). Slinkies can do transverse and longitudinal waves.

For water waves, if you have ripple tanks you will probably have gadgets that came with them, including vibrating bars for making beams of plane waves, and an instruction manual. In most cases, reflections are complicating (but interesting) factors. Remember that water waves have non-linear superposition when amplitude is not << depth - much loved by surfers, but a complication for superposition.

For ropes, rubber ropes (we use the flexible hose that your chemistry lab may use for the Bunsen burners) have some advantages. One is that the length can be used to control the tension for reproducibility. Remember that ropes become non-linear media when the displacement changes the tension (another advantage for rubber hose). Comparing stretched ropes (observable motion at low tension and large mass) with musical string instruments (which do the same thing too fast to see but fast enough to hear) is a useful teaching exercise.
Musical string instruments give convenient examples of standing waves in stretched strings. These are very good for v = f*lamda (and for the effect of tension and string mass per unit length on v). The electric guitar has a few ~ velocity transducers (pick-ups) built-in, and is a familiar context for many students. A violin or bass bow is useful for exciting quasi continuous standing waves. Harmonics are easier with a bow. (Get fibreglass ones for long life.) (For more on harmonics, see our page strings).

A stroboscope, running at a frequency of n/m times that of the vibration (n and m integers) can be used to 'freeze' the motion of a periodic vibration e.g. a string in a combination of modes or a drum head in a single mode*. If n = 1, one image per cycle is seen. For neurological reasons it is unwise to look at a strobe flashing at frequencies between 2 and 10 Hz.
* With the approximate exceptions of timpani and tabla, drum head mode frequencies are not at rational fractions. However, the second lowest mode often lasts lower than the others.

"present and analyse displacement-time graphs for longitudinal and transverse wave motion"
Direct experimental measurements are tricky, although one can sketch qualitative observations of travelling and standing waves in a slinky or a rubber hose. The envelope of standing waves in guitar strings can be seen and sketched. Velocity sensors (electric guitar pickups) and pressure sensors (microphones) are much easier for measurements. Observing that the velocity has no DC component (the string doesn't fly away and there is no wind), students can integrate the signal graphically, or you can integrate it on an RC circuit to display displacement (from pressure to displacement is two integrations).

Experiments with mobile phones
Turn on, wrap in Al foil and phone its number. Unwrap gradually. Demonstrates that the good conductor reflects EM waves. More importantly, it will also stop the phone ringing during class.

Light rays and geometrical optics
Laser diodes are a cheap way of getting a beam with low divergence (buy directly from an electronics or hobby store for several $ including power supply: just add a battery. Or else buy assembled in laser pointers). Can use to demonstrate ray representation of fibre optics. They're also fun toys for a while and may seem more interesting than light boxes (lamp source and cylindrical lens, gives a vertical plane of light). For plotting on paper, light boxes are immediately usable. A laser can also make a vertical plane of light by passing it through a cylindrical lens (axis horizontal). A suitable lens is a short section of plexiglass rod. If you have light boxes, you probably also have a kit that goes with them: hemi-cylinders for Snell's law, 2D lenses for making optical instruments, cylindrical mirrors et hopefully cetera. (By the way, cylinders of perspex make good model raindrops to show how rainbows form.)

Some notes about a guided investigation
This was one of the FAQ's and so I felt obliged to answer it: How to avoid the recipe lab exercise, but still guide an investigation? I have almost zero experience in teaching high school students. Mosr readers of this document will have formal qualifications and extensive experience in doing just that. Further, the labs that I have tried to run along the lines tried here had relatively small numbers of students and taught different material. So it is with temerity that I offer some suggestions about trying to make an investigation less recipe based. I shall use Snell's law (not widely considered exciting) as an example. For me, the aim of teaching Snell's law is less important than teaching the method of careful observation, improvement of measurement technique, generalisation and testing.

Some demonstrations to arouse interest, e.g. dismantle camera, use telescope/ microscope, set fire to paper using lens.
Some initial contextual question(s): Where do you find lenses? How does a lens work? Where would we be without them? Who invented them? Who invented ?
Does light travel in straight lines? When?
When it doesn't, what happens? Explore and generalise qualitatively. Some questions: why does the water look shallower? why does the surface of the water look silvery and strange to swimmers looking up?
What are the consequences for vision? For natural phenomena? For optical instruments? (higher performance; mirages, distorted sun, green flash; spectacles, cameras, telescopes)
Paper work. What sort of relations might be involved? If you draw a diagram of wave fronts incident on a surface, what would light bending at an interface look like?
How can you obtain some relevant quantitative data using the gear we have here?
What makes the arrangement complicated? Are there ways you can reduce/eliminate the complications or number of things to measure?
What will be the measurement errors? In particular, what is the largest measurement error (protractor? ruler? beam centre estimation?) and is there any way of making it smaller?
Are there some errors that can't be reduced and thus impose a limit to the precision of your experiment? If so, can you reduce the other errors to this level?
Can you get a quantitative rule out of this? If different teams find different rules, what are the cases where they disagree? Can you test them to see which is supported experimentally? (If they don't disagree, can they be proved to be identical?
Suppose that you don't get Snell's law, or that you get a silly value for n, what then? Could the text books be wrong? Could we have made an error in interpretation, or a systematic error? How badly does Snell's law fit our data? How does the difference compare with the error?
Application: back to some of the examples, draw qualitative diagrams to explain operation. How does a lens or a mirage work? Do a quantitative ray diagram?

Some useful gear that is either or both cheap and readily available.

A few web resources:

Some notes about the physics of speech.