17.5 Sound Interference and Resonance: Standing Waves in Air Columns

In astronomy, we can determine the speed of light from distant galaxies.

The light of the galaxies is shifted to a lower wavelength as they move away from us.
The age of the universe has been estimated using information from far away.

When the sound source is moving and the observer is stationary, the perception of sound needs to be compared.

Do you rely on the Doppler shift to help you when driving a car or walking near traffic?

If I am driving and hear the ambulance sirens, I would be able to tell when it was close and if it had passed by.

This would let me know if I needed to pull over.

Constructive and destructive interference can be used to cancel out outside noises.

One way to prove something is to observe interference effects.

Sound is a wave and we expect it to exhibit interference, such as the beats from two notes playing at the same time.

The figure shows how sound interference can be used to cancel noise.

For the entire passenger compartment in a commercial aircraft, larger-scale applications of active noise reduction by destructive interference are contemplated.
A second sound is introduced with its maxima and minima reversed from the incoming noise after a fast electronic analysis is performed.
Positive and negative gauge pressures add to a much smaller pressure, which creates a lower-intensity sound.
It is possible to reduce noise levels by up to 30 decibels using this technique.

A sound wave opposite to the incoming sound is created by headphones.

The headphones can be more effective than passive ear protection.
The record-setting, around the world nonstop flight of the Voyager aircraft, used headphones to protect the pilots' hearing from engine noise.

Sound resonances are caused by interference.

The only frequencies that interfere with standing waves are the resonant frequencies.
The resonance and standing waves of a great singer's voice play a vital role.

It is proof that something is a wave if you observe interference.

Experiments showing interference established the wave nature of light.
When electrons were scattered from crystals, their wave nature was confirmed to be exactly as predicted by the wave characteristics of light.

If the tuning fork has the right frequencies, the air column in the tube vibrates loudly, but at most frequencies it doesn't.

The air column has certain frequencies.
The figures show how a resonance is formed.
A sound travels down the tube and bounces off the closed end.
The reflected sound arrives back at the tuning fork half a cycle later if the tube is just the right length.
The tube has a standing wave in it.

A tuning fork causes a tube to close at one end.

The tube is moving.

A tuning fork causes a tube to close at one end.

The tube has a closed end.

A tuning fork causes a tube to close at one end.

The sound from the tuning fork can be interfered with if the length of the tube is not right.
The interference forms a standing wave.

A tuning fork causes a tube to close at one end.

A graph of air displacement along the length of the tube shows no at the closed end and a maximum at the open end.
The standing wave has one-fourth of its wavelength in the tube.

The length of the tube is equal to the distance from a node to an antinode.

It is best to consider how the air column is vibrating, not how it is being caused.

A standing wave is created by a vibrating tube.

There are a lot of shorter-wavelength and higher-frequency sounds in the tube.

Specific terms are used for the resonances.
The fundamental is the first, the first overtone is the second, and so on.

A tube is closed at one end.

There are no air displacements at the closed end.
Three-fourths of the wavelength is equal to the length of the tube.
This is the first overtone.

A tube is closed at one end.

There are no maximum air displacements at the closed end.

In a variety of combinations, the fundamental and overtones can be present at the same time.

The middle C on a trumpet has a different sound than the middle C on a clarinet, both instruments being modified versions of a tube closed at one end.
The fundamental frequency is the same, but the overtones and intensities are different and subject to shading by the musician.
The mix gives various musical instruments their distinctive characteristics, whether they have air columns, strings, sounding boxes, or drumheads.

The sound of the vowels can be evoked with simple resonance.

The difference in frequencies in speech between men and women can be traced back to the shape of the larynx at puberty.

The throat and mouth form an air column closed at one end that vibrates in response to the sound in the voice box.

The spectrum of overtones and their intensities vary with mouth shape and tongue position.
It is possible to replace the voice box with a mechanical one.
Different voices are recognizable by variations in basic shapes.

Let's look for a pattern in the frequencies for a tube that is closed at one end.

The first overtone is the third Harmonic.

A pattern can be generalized in a single expression.

The speed of sound and temperature are related to the resonance frequencies.

Musicians commonly bring their wind instruments to a room temperature before playing them because of the dependence on this dependence.

The length can be found from the relationship, but we need to find the speed of sound.

The air temperature can be used to find the fundamental Frequency.

This equation can be solved for length.

Use the speed of sound to find it.

The values of the speed of sound and frequency should be entered into the expression.

Many wind instruments have modified tubes that have finger holes, valves, and other devices that can be used to change the length of the air column.

Tuba horns require long tubes that are coiled into loops.

Whether this overtone occurs in a simple tube or a musical instrument depends on how it is stimulated to vibrate.

The trombone only makes overtones and does not produce fundamental frequencies.

There is a tube that is open at both ends.

Organ pipes, flutes, and oboes are examples.
Tubes that are open at both ends can be analyzed in the same way that tubes that are closed at one end can be.
The waves form as shown.

The fundamental and first three overtones of a tube are shown.

A tube that is open at both ends has a fundamental Frequency that is twice what it would have if closed at one end.

It has a different spectrum of overtones than a tube closed at one end.
If you had two tubes with the same fundamental frequencies, but one was open at both ends, and the other closed at one end, they would sound different.
Middle C would sound better played on an open tube because it has multiples of the fundamental as well as odd.
There are odd multiples in a closed tube.

strings, air columns, and atoms are some of the different systems where resonance occurs.

A system at its natural frequencies is called resonance.
When the system can no longer be described by Hooke's law, the energy is transferred quickly to the system.
There is a distorted sound in certain types of rock music.

Wind instruments use resonance in air columns to amplify their sounds.

Air resonance is used in other instruments to amplify sound.
The vibrating string creates a sound that vibrates in the box and gives the instrument its characteristic flavor.
The more complex the shape of the box, the greater its ability to amplify.
Adding water can change the resonance of the pot.

Violins and guitars use resonance in their sounding boxes to amplify and enrich their sound.

The sound boxes and air are supported by the bridge.

Since prehistoric times, resonance has been used in musical instruments.

The marimba uses gourds as resonance chambers.

We emphasize sound applications in our discussions of resonance and standing waves, but these ideas apply to any system with wave characteristics.

For air columns, vibrating strings have the same fundamental and overtones as air columns.
The wave character of electrons is what causes the resonances in atoms.

The fundamental and excited states of their waves can be viewed as standing waves.

Waves apply to a wide range of physical systems.

Explain how noise-canceling headphones are different from standard headphones.

A physical barrier blocks sound waves.

Louder sounds can be reduced by using noise-canceling headphones.

The closed end of the tube has the wave's open end at it.

One-fourth of the wavelength of the wave is equal to the length of the tube.
We can determine the length of the tube if we know the wavelength of the wave.

You can see sound waves.

You can hear how the wave changes by adjusting the volume.
Listen to what she hears.