Episode 319: Preparation for superposition of waves topic
Waves add together by superposition; that is, when two or more waves meet, the resultant is the algebraic sum of their displacements. Although this is a mathematical idea, this topic has many practical, hands-on activities once you begin to discuss the consequences of superposition (diffraction and interference effects). Since you will be working with light and sound, there are some great visual and audio effects.

You may come across two different approaches to this topic: a geometrical one and a conceptual one. The former starts with single slit diffraction, develops this to (Young’s) two slits and thence to multiple slit diffraction gratings. The latter first investigates superposition itself, followed by ‘interference fringes’ then diffraction.

Here we adopt the conceptual approach.

Many demos are suggested using many different types of wave motion. The first time you set these up keep diagrams or exact notes of what works best with the actual equipment you have to hand. This will save you time on the next occasion you teach this topic!

 A stick wave ‘machine’ is useful. It consists of two parallel strings with many sticks threaded on in the plane defined by the two strings. The strings are held at each end to provide sufficient tension. Giving the stick at one end a twist produces a slow ripple as the torsional wave travels down the strings.

Lasers
You will find it useful to work with lasers in some of the activities described here, so it is a good idea to familiarize yourself with any available lasers, and to ensure that you know how to use them safely.

Laser light is particularly suitable for optical work. He-Ne gas lasers used in schools and colleges have a wavelength of 633 nm. Laser lines and laser pointers can also be used, but check that they are ‘Class 2’ permitted for use in schools and colleges. Laser pointers tend to need new batteries quite often when used for experiments rather than ‘pointing’.

Laser diodes can now be bought from various suppliers. For example, a Class 2 laser diode from Maplin (www.maplin.co.uk) costs about £ 20 and runs off a 3 V battery. It can be mounted it in a Colorail Centre Bracket 19 mm diameter from B&Q (they’re used for mounting a curtain pole/rail). With a set of taps and dies put three bolt holes in it at 120 degree intervals and then put in three bolts. This gives an excellent mounting (and adjustment) system for the laser diode and also acts as a good heat sink, which is needed for fairly continuous operation. Make sure that a laser safety label is prominent alongside the device.

Safety with lasers
Never shine laser light directly into the eye, or allow it to reflect from a shiny surface. Direct the light onto the ceiling: all students in the room can see a ‘spot’. The beam has been diffusely reflected into all angles, so the intensity in any one direction is low and safe to view.

Ripple tanks
It’s worth practicing with a ripple tank before going public in front of the class. Here are some tips for setting up a ripple tank with an OHP.

Add a single small drop of detergent to the water - this helps to “wet” the wave bar.

Adjust the position of the wave bar and/or its frequency so you get standing waves between it and the adjacent edge - the resulting increased amplitude of the wave bar helps to get better amplitude waves where you want them.

Use a variable power supply to control the illumination of the OHP for optimum contrast.

It’s worth taking some care to level the tank - varying water depth leads to refraction if the wave bar in not perpendicular to the long axis of the tank. Even with good alignment, if the depth changes this leads to a change of wave speed and hence wavelength. (You will notice optimum standing waves when the wave bar is parallel to the short side.)

Main aims
Students will:

• Use the principle of superposition of waves to determine the resultant displacement of two or more waves
• Understand how diffraction and interference effects result from superposition
• Use the equations for single, double and multiple slit diffraction
• Use double and multiple slit diffraction to determine wavelength
• Explain how standing waves arise from travelling waves
• Use standing waves to determine wavelength and wave speed

Prior knowledge
Students should have studied the basic representation of sinusoidal waves. They should be familiar with the wave speed equation c = fl.

It will be helpful if they are familiar with some aspects of trigonometry (small angle approximations sin q ~ q ~ tan q, maximum value of sin q = 1 etc; simple triangle trigonometry).