In explaining the electron orbits in the Bohr atom, de Broglie's principle of particle wave duality allows you to treat the electrons as waves of wavelength nλ = 2πr where r is the radius of the orbit. Then the only orbits allowed are those which are integer...
Standing sound waves in a glass pipe are made evident by the fountains of kerosene inside the pipe.
What it shows:
The air inside a very large glass pipe (partially filled with a fluid) is acoustically excited into a standing wave. Once resonating, the locations of the velocity antinodes inside the pipe are dramatically made evident by the vigorous agitation of the fluid, resulting in fabulous foaming frothing fountains of fluid. The velocity of sound can also be determined by noting the resonance frequency and measuring the distance between antinodes....
An aluminum rod, supported in the middle, rings for a long time in its longitudinal mode.
What it shows:
Longitudinal standing waves in solids.
How it works:
A metal rod is not unlike an organ pipe with both ends open. Holding it exactly in the middle will force the simplest, or fundamental, mode of vibration -- the ends will be free to vibrate maximally and the center will be a node. The fundamental frequency happens to be 2.26 kHz. As with a pipe open at both ends , the rod will vibrate at all the odd as well as even...
Generation of a standing wave by reflection from a fixed end.
How it works:
A two person demonstration using a 2m (2cm diameter) steel spring. 1 One party acts as the fixed end, standing holding the spring rigidly at chest height. The other sends the pulses down the spring by vigorous up-and-down movements. The frequency is adjusted to set up a standing wave from the fundamental up to whatever you're capable of (see Comments). Amplitudes of...
Rods attached to metal spine; transverse wave generator shows the reflection of waves free, fixed, terminated and transition boundaries.
What it shows
Mechanical demonstration of transverse standing or traveling waves using the Shive wave machine.
How it works
The Shive wave machine consists of a series of horizontal metal rods 1.25 cm apart coupled by a torsion wire. A pulse can be sent down the machine by displacing the end rods (when doing this by hand, pull down on more than one rod as the connections are delicate and do break). The far...
A large square metal plate, supported and harmonically driven at its center, is made to vibrate in any one of its numerous normal modes of vibration. As with the regular Chladni Plates, the two-dimensional standing wave patterns are made visible by sand accumulating along the nodal lines. What is different in this demonstration is that a multitude of resonances (across the entire audio range and lower ultrasonic frequencies) can easily be excited. Being a two-dimensional oscillator, the various resonance frequencies are not simply multiples of the...
Accumulation of sand at nodes of vibrating plate reveals resonance patterns.
What It Shows
A Chladni plate consists of a flat sheet of metal, usually circular or square, mounted on a central stalk to a sturdy base. When the plate is oscillating in a particular mode of vibration, the nodes and antinodes that are set up form complex but symmetrical patterns over its surface. The positions of these nodes and antinodes can be seen by sprinkling sand upon the plates; the sand will vibrate away from the antinodes and gather at the nodes.