# Physics 3.3 AS91523 Demonstrate understanding of wave systems.

Link to NZQA information relevant to this standard.

Links are provided to demonstrations that can support the material in the Achievement Standard. Some discussion is given below of how to use the resources in the classroom.

#### Interference (quantitative) of electromagnetic and sound waves, including multi-slit interference and diffraction gratings.

Diffraction and interference are really just different manifestations of the same underlying physics, and that is the principle of superposition that tells us the displacement of a medium due to two waves is just the sum of the individual waves. In other words, waves add and cancel. This is the underlying physics. One can show simple diagrams of this that are seen in many textbooks, something like this.

But is this really true? Can waves cancel? Can two louds make a quiet, can two brights make a dark, so to speak? Before launching into the geometry, show students it really works. Besides the usual double-slit interference where the dark bands show light waves cancelling (two brights make a dark), here are some useful resources for that: Sound Interference,  Diffraction and Interference of Water WavesRipple Tank.
When you are ready to move on to quantitative work, you can do the standard double slit interference experiments quantitatively and then use the These very inexpensive and easy to use diffraction gratings are great for both qualitative and quantitative experiments and activities.

Note for teachers: Light or sound waves carry energy. If two light or sound waves cancel, where does the energy go? Answer.

#### Standing waves in strings and pipes

One can begin with transverse and longitudinal pulses on a slinky. Show for example that transverse wave pulses are inverted upon reflection from a fixed end. One can then explain that a wave sent continuously down the spring will reflect back continuously (inverted) and the interference of the two waves can produce a pattern called a “standing wave.” Show the standing waves on the slinky, or use a very long spring for more dramatic effect. Then reinforce this with a good standing wave simulation. We recommend the ones produced by Walter Fendt here.

One can then move on to making Standing Waves on a Wire using a signal generator to wiggle the wire near a magnet. Quantitative study of standing waves is easy to set up this way and can be quite effective. Victoria University has developed a nice version of this that can be made by teachers in a school lab.

You can then move on to setting up standing sound waves in a tube. There really are nodes in the tube! And sound really does reflect off of an open end! A write-up of this demonstration is coming soon. It is very inexpensive to construct if you have a data logger and microphone.

If you want a very impressive demonstration, have a look at the resource. Note that a careful analysis of this experiment is not trivial at all.

#### Harmonics; resonance; beats

Resonance is one of the most important and also one of the most misunderstood concepts in physics. Essentially when you drive a system (mass on a spring, pendulum, …) at particular frequencies you get a very strong response. Driving the system at other frequencies does not produce a strong response. A detailed discussion of this with some additional very advanced material is coming soon. Using a pendulum is perhaps the best way to explain resonance. When you tap the pendulum at its resonant frequency, the oscillations become huge. At any other frequency they do not. Does a pendulum have more than one resonant frequency? Is the resonant frequency the same as the natural frequency? All of that will be discussed in the advanced materials.  Meanwhile have a look at Tuning Fork Resonance.

Note that standing waves are a resonant phenomenon. If you make a standing wave on a spring the oscillations are huge even though you shake the spring gently (at one of the right frequencies). At other frequencies you will shake the spring pretty hard and get very little waves.

Beats are closely related to standing waves. With a standing wave, the two constituent waves have the same frequency and travel in opposite directions. They cancel at all times in some places. With beats, the two waves have slightly different frequencies and cancel in all places at some times. See Beats, Combining Sounds, Tuning Fork Beats.

#### NZQA: “Doppler Effect”

The Doppler Effect can be studied in school labs qualitatively very easily. See for example the Doppler Ball. With a bit more difficulty it is possible to do quantitative work with Doppler shifts in sound waves. See for example Doppler Ball Frequency Shift Quantitative.

Note for teachers: Although this goes beyond the curriculum, note the Doppler Effect for light is qualitatively similar to the Doppler Effect for sound, but it is quantitatively different. An approaching siren is heard at higher frequency, and an approaching light is seen at higher frequency (blue shift). But the formulas are different. Why? Answer.