# Sound Waves

Use this site to demonstrate or explore basic concepts of waves and wave superposition, in the context of sound waves.

While this site focuses on sound, the concepts met here apply to any type of wave motion.

Caution! The sounds produced on these pages can be quite piercing at high volumes.  Start with your device volume set low, then adjust accordingly.

## Sound Waves Page

Explore the relationships between frequency, wavelength and pitch, and between amplitude and volume.

There is a button to toggle the sound (a sine wave) off/on for convenience. The pitch of the sound ranges from 220 Hz to 880 Hz, a range of two octaves (A3 to A5 on a piano keyboard).   Adjust frequency/wavelength with the horizontal slider and amplitude with the vertical slider to see their effect on the wave shape and on the sound produced.  The sound volume also depends on your device's volume settting.

The relationships between values are accurate, but absolute values are not.  For example, increasing the pitch by one octave does double the frequency and halve the wavelength, but the frequency of the vibrating particle on the screen is much lower than the actual frequency of the note being sounded.  Similarly, wavelengths displayed on the screen are arbitrary and depend partly on the screen dimensions.  The true wavelengths of the sounded notes range from approximately 160 cm (A3) to about 40 cm (A5).  The intention here is to make patterns and relationships easy to see, not to accurately reproduce real values.

Vary the frequency/wavelength and amplitude of two separate sine waves, and view the resulting sum of the two.

The longer, left hand slider below each component wave adjusts the frequency/wavelength of the wave.  The shorter, right hand slider adjusts the amplitude.

There is a button to toggle the sound of each component wave off/on.  Doing so does not remove the wave from the summation.  It just mutes the sound for convenience.  To remove a component wave from the summation, reduce its amplitude to zero.

Each sound ranges in frequency from 220 Hz to 1660 Hz, a range of three octaves (A3 to A6 on a piano keyboard).  The particles on screen are oscillating at a much lower frequency than that of the sound being produced in order to make their motion clearer.

The sound volume also depends on your device's volume settting.

This page is similar to the "Add 2 Waves" page, except that it adds three component waves.  The controls are identical to those on the "Add" 2 Waves" page.

Three component waves can produce more interesting shapes than two.

## Beats Page

This page is similar to the "Add 2 Waves" page, except that it is modified to make the beats effect more obvious.

More wavelengths fit on the graphs, making the beats patterns clearer as the two frequencies approach each other.  The oscilating partciles have been removed, since the focus here is on the superposition pattern.  Frequencies range from A above middle C (440 Hz) to the E above that (~659 Hz).

As two frequqncies approach each other, they add so as to produce a pattern where they cancel out them reinforce each other in a regular pattern.  We perceive this pattern as regular fluctuations in the volume of the sound.  As the two frequencies get closer to each other, these beats are heard further apart, disappearing completely when the frequencies exactly match.  Musicians commonly make use of beats when tuning their instruments.

The controls are identical to those on the "Add" 2 Waves" page.

## Phase Page

Two sine waves are produced with the same frequenciy (440 Hz) and the same amplitude.  Use the slider to shift the second wave up to 180° out of phase with the first.  You can see the sum of the two waves on the bottom graph.  The button turns the sound on/off.

What does a phase shift mean in terms of the motion of the particles?  What effect does it have on the sound heard?

Can you think of relevant applications of this knowledge, e.g. for positioning of microphones, or wiring of speakers?

## Hearing Page

Be particularly careful if using headphones.

Proper hearing tests must be conducted under controlled conditions by a trained professional to be accurate.  There are far too many variables that cannot be controlled when using this web page for the result to be taken seriously.

The best use of this page is probably to demonstrate how hearing range decreases with age.  As the frequency is increased, older people will usually reach the point where they can no longer hear the tone before younger people do.  A reduction in the range of hearing with age is normal.  The range of human hearing is commonly stated to be 20 Hz to 20,000 Hz.  In reality, you probably won't get close to 20,000 Hz on this test.

Begin by making sure your device volume is not too loud, and that the starting frequency is the default 440 Hz (A4 on a piano keyboard).  The small slider further controls the volume of the tone.  Use the button at the bottom left to turn the tone on or off.  Adjust the volume of the starting tone to a comfortable level.

Slowly move the large slider, increasing the frequency until you can no longer hear the tone.  That, in theory, is the upper range of your hearing, but remember that this is not an accurate test.

Resist the temptation to increase the volume as you near your upper limit.

If you cannot hear the starting 440 Hz tone, check the volume controls on your device and on the page before assuming that you are deaf.