Helmholtz Resonator – Music from a bottle

1. Helmholtz Resonator – Music from a bottle Picture Area • These resonators are very different from Organ pipes - relatively small bottles can make very low tones. • Turbulence from the air jet excites the air in the neck of the bottle which vibrates in and out. • Adding water to the bottle reduces the volume V and increases the pitch of the tone. Musical instrument Helmholtz resonator

2. Open ended Tube Closed ended Tube Organ Pipe Resonators – Music from a tube: Boomwackers Closed end • These resonators are simply tubes or pipes • At an open end the air vibration/oscillation (along the tube) is maximum (Anti Node). • At a closed end the air cannot vibrate/oscillate so there is a node. • This sets up the standing waves that resonate in the tubes. • For a set tube length L the fundamental (what you will mostly hear) wavelengths are: lopen =2L and lclosed = 4L , so lclosed is 2x lopen! Or the fundamental frequencies are nopen = c/lopen = c/2L and nclosed = c/4L , so nopen is 2x nclosed , And the open ended is one octave above (2 x ) the closed ended. nC = 256 Hz -middle C lC = 340/256 (m/s*s) = 1.3 meters For Open tube L= 2.6 m For Closed tube L= 5.2 m !!

3. Open ended Tube Organ Pipe Resonators – Music from a tube: Singing Tubes • These resonators are simply tubes or pipes • At an open end the air vibration/oscillation (along the tube) is maximum (Anti Node). • At a closed end the air cannot vibrate/oscillate so there is a node. • This sets up the standing waves that resonate in the tubes. • For a set tube length L the fundamental (what you will mostly hear) wavelengths are: • lopen =L/2 and lclosed = L/4 , • so lclosed is 2x lopen ! • Or the fundamental frequencies are • nopen = c/nopen = 2c/L and nclosed = 4c/L , • so nopen is 2x nopen , • And the open ended is one octave above (2 x ) the closed ended. Open tube L=74 cm l fundamental = 2*74= 1.48 m, l 1st = 74 cm f1 = 230 Hz fundamental, f2 = 460 Hz, f3 = 690 Hz f4 = 920 Hz

4. Sympathetic Vibrations Sympathetic vibrations – one vibrating item can cause another with same natural frequency to vibrate as well. For the wire demo, natural frequency is based on length of wire. The shorter wires have higher natural frequency. Vibrating long wire causes only other long wire to vibrate. Short wire causes only short stick to vibrate. SYMPATHETIC TUNING FORKS These tuning forks (286 Hz) are mounted on resonance boxes. The size of the air column in these boxes is so chosen that it will reinforce the same sound that the tuning fork gives. That is, the box acts as a closed organ pipe and the length of the box corresponds approximately to one-quarter of a wave in air of the sound produced by the fork. Place the resonance boxes aligned and with their openings facing each other. Now strike one fork sharply with the provided rubber hammer. This throws the box to which the fork is attached into strong vibration. The air column will also be set in vibration and all the air immediately around will be set in vibration. This vibration sets the air column in the other box into vibration sympathetically. This air column in the second box causes the tuning fork to vibrate. The second instrument is thus set into vibration by the first instrument. Prove that one fork sets the other into vibration, by striking one fork, let it vibrate for a few seconds and then hold its prongs. The same sound will still be heard!

5. Tuning Fork Waves Simple Idea: Placing a vibrating tuning fork in water allows one to see waves created by this vibration. Complication: The tuning fork vibrates at around 128 Hz. The speed of sound in air is 343 m/s. The wavelength of these waves then are about 2.7 m. In water the speed of sound is about 1500 m/s – which leads to a wavelength of 12 m! However, the wavelength of the standing waves seen in the water are on the order of millimeters to centimeters – something else must going on to account for a wavelength this small! Water (ocean) waves a incredibly complex and not fully described by an model. However, in general, the velocity of a wave in water depends on wavelength and possibly water depth if the water is shallow enough. Also, however, there are two main types of waves. Gravity waves in the ocean are due mainly to the force of gravity and inertia. But there is also a second type, mainly present for very small wavelengths on the order of centimeters. These are called “capillary waves” and are due primarily to the force of the surface tension of the water. They have the property that, as wavelengths get shorter, their speed increases! This is called anomalous dispersion. It is very different than, for instance, electromagnetic waves traveling in a vacuum, where speed is constant and as wavelength decreases, frequency simply increases. As amplitude for wave increases, goes from trochoid shape to sharper peaks – these reach a limit and, after this limit, shoot water from peaks. This is source of initial water bubbles when tuning fork is placed in water – the high amplitude brings wave to limit of peak shape.

6. Standing Waves General String T = tension m = mass L = length Supplemental Wave Info • Standing waves: • Node: point that doesn’t move. • Anti-node: point that moves a lot. • Types: • Transverse and Longitudinal • Propagation Speed: • Inversely related to Density