Resonating Air Column; Metal Rod

Resonating Air Column; Metal Rod

Description

A tuning fork held above a column of air causes a resonant sound for certain column lengths. A metal rod held at its center vibrates with a loud, characteristic sound when "stroked." The frequency of the sound can be changed by changing the point of support.

Set

Electrons exhibit wave properties. Students usually profit from concrete illustrations of wave phenomena.
When a vibrating tuning fork is brought near the open end of a tube closed at one end, a strong reinforcement of the tuning fork frequency will be heard if the length of the air column in the tube is appropriate. This phenomenon is called resonance. It is observed when the sound waves reflected from the closed end of the tube return to the top of the tube in phase with the new waves being produced by the tuning fork. The direct and reflected waves combine their effects. Very noticeable increases in sound intensity can be heard at certain frequencies in conjunction with certain tube lengths.
The various possible frequencies at which a tube may resonate are definite and fixed in value. They depend upon the length of the pipe and the velocity of sound in air. In a cylinder of air, the length (L) of the column of molecules vibrating must be some odd number multiple of the wavelength of the tuning fork oscillation:

n l = 4 L
In this equation: n = an odd integer (1, 3, 5, ..); l is the wavelength of the sound wave; and L is the length of the air column.
The relationship between the frequency and wavelength of the sound wave is given by the equation:

f l = u
In this equation: f is the sound frequency in Hertz (cycles per second, as stamped on a particular tuning fork); l is the wavelength of the sound; and u is the speed of the sound (approximately 346 meter/second in air at 300 K).
It is important to note that there is a relationship between the length of path in the closed tube and the wavelength (or frequency) of vibration. Only certain frequencies of oscillation "fit" the path length, and resonate.

Procedure

Fill the large cylinder about two-thirds full of water.
Set the resonance tube into the cylinder. By doing so, you will allow the water to close one end of the tube.
Choose a tuning fork.
Strike it on the rubber stopper, and bring it over the open end of the resonance tube. Hold the tuning fork in the position that allows the tines to vibrate toward and away from the surface of the water in the tube.
Slowly change the level of the tube by continuing to hold the fork in one hand and raising the resonance tube with the other. Do not allow the vibrating tuning fork to touch the cylinder.
Change the level of the resonance tube until you hear strong resonance. Continue changing the level of the tube to catch harmonic repetitions (i.e. different octaves) of the same resonating frequency.
Measure the length of the tube.
Repeat with several other tuning forks with different frequencies.
Have the students compare the air column height that effectively resonates any given tuning fork wave.
If other resonance tubes are available, you may wish to repeat the demonstration with a different path length as well. This variation can also be achieved to a certain extent by changing the water level in the large cylinder.
Prepare a metal rod notched at the half length and quarter length points.
Rub some rosin between your thumb and first finger.
Grasp the rod between your thumb and first finger at the half-length mark, and stroke the rod. Note the sound.
Grasp the rod between your thumb and first finger at the quarter-length mark, and stroke the rod. Note the sound.

Handout Makeup

Name _____________________________ Class _______

Teacher______________________________

DoChem 028 Resonating Air Column; Metal Rod

Lower pitch tones correspond to longer wavelengths.

Watch and listen to the movies.

Describe the sound changes as the tube is raised.
Predict the effect of using an inner glass tube having a diameter 50% larger than the one used to gather data.
Which pitch is lower--the sound the rod makes when grasped at the middle or the sound it makes when grasped at the 1/4 mark?

Which sound has the longer wavelength? Explain the result.

Teachers Guide

Purpose

To illustrate resonance of a sound wave in a confined path.
To illustrate resonance frequency of an object.

Materials

1 large glass cylinder (at least 35 cm tall)
1 open-ended glass cylinder or resonance tube (60-cm to 80-cm long; small enough diameter to fit into the first cylinder)
several tuning forks (256-512 Hz)
1 large, single-hole rubber stopper mounted on a dowel or pencil
1 support stand, single buret clamp
1 ruler or meter stick
tap water, food coloring
1 metal rod, uniform, 1.5 cm diameter, 1 meter long, with small notches at exactly the half-length and quarter-length points
rosin (bow rosin used for violins works well)

Lab Hints

A 500-mL or 1-liter graduated cylinder works very well for this experiment.
The open-ended glass resonance tubes can be purchased from major scientific suppliers. Cylindrical plastic tubes may also be used.
Make certain that the room is very quiet while this demonstration takes place. The clarity of the resonating sound will be much enhanced.
It is a little tricky to coordinate the motion of raising the resonance tube while also holding a vibrating tuning fork. A couple of practice trials are recommended.

Time

Teacher preparation: 15 minutes

Presentation: 15 minutes

Hazards

The sound emanating from the metal rod can be painfully loud.

Precautions

Strike the fork on the rubber stopper. Do not strike the tuning forks against something hard (e.g. the edge of a table). Hard blows damage the tuning forks and generate a "tinny" sound which will overpower the subtler resonance frequency that is most desired.
Do not permit the sound intensity from the metal rod to cause discomfort. Warn students with sensitive hearing to protect their ears.

Disposal

Discard water at the sink. Save other materials for future reuse.

Presentation?

Presentation Question:

Predict the effect of using an inner glass tube having a diameter 50% larger than the one used to gather data.
- The formula does not account for the diameter of the closed tube so, to a first approximation, one predicts that there is no effect. Test this for your students to verify the outcome. There is an effect of the tube diameter; the larger the tube diameter, the shorter the length of closed tube necessary to achieve resonance. The effect is a small one.

Background

Electrons act like waves. The wavelength depends upon the mass and velocity of the electrons according to the following relationship:

l = (h/mv)
In this equation: h is called Planck's constant, 6.62 x 10^-34 Joule x second; m is the mass of the electron; v is the velocity of the electron; and l is the wavelength of the electron. The product mv is the momentum of the electron. For an electron moving at high speed, the denominator, mv, is large and the wavelength is small. The faster an electron moves, the shorter is its wavelength.
The development of the theory of atomic structure into wave mechanics has shown that the Bohr picture of the atom with sharply defined electron orbits is incorrect. In an alternate model to the Bohr atom, called quantum mechanics, the single electron in a hydrogen atom is described in terms of its wave-like characteristics.
Students may ask why neither quantum effects nor wave aspects are seen in the natural events that we normally observe. For example, suppose you swing a rock in a circle at the end of a string. There do not appear to be discrete quantized orbits; instead, any radius or velocity is possible. Also, there is no obvious wave appearance. The fact is that the rock does have quantum and wave properties, although these are not perceptible to us. Calculations show that, for a large object like a rock these quantized states are so close together that a human cannot tell them apart. As matter waves attain longer wavelength, the quantum distinction between adjacent states starts to become apparent.

Conclusions

Only certain column lengths resonate in the experimental apparatus.
The same kinds of resonance phenomena found for sound waves are expected for particle waves.
Electronic properties are explained in terms of wave-like characteristics. Quantum theory, used to describe electrons in atoms, predicts specific, quantified frequencies for electrons.

Makeup Ans.

The volume of the sound increases and then decreases and increases again. At the maximum, the sound is much louder than the soft sound.
See presentation question.
The sound when grasped at 1/2 mark has the lower pitch and longer wavelength. The length of the rod allowed to vibrate freely is 1/4 the total length when held at the 1/4 mark and 1/2 when held at the 1/2 mark. The wavelength of the resonant frequency is related to that length.

Key Words

resonance
frequency
wavelength
energy
quantum effect
model for quantum effect