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### Frequencies and Wavelengths of Sound

by Ron Kurtus (15 March 2008)

Since sound is a compression waveform, its frequency is the rate that the maximum compressions pass a given point in a second. The unit of frequency is the hertz (Hz), which means cycles per second. Infrasound consists of very low frequency sound, beyond the range of hearing of humans. Audio frequencies are those that can be heard. Ultrasound consists of very high frequencies, again beyond the human range of hearing. Knowing the speed of sound in air, you can convert frequencies into wavelength.

Questions you may have include:

• What are the frequencies for infrasound?
• What are the audio frequencies and wavelengths?
• What is ultrasound and how is it used?

## Infrasonic frequencies

Infrasound is transmitted with a frequency that is too low to be heard by a human. The range of infrasound usually starts at 16 hertz (Hz) and goes down below 0.001 Hz.

One major feature of infrasound is that it can travel great distances and go around objects smaller than its wavelength. Elephants have been known to communicate with other elephants that are many miles away with these low frequency sounds that humans cannot hear. Earthquakes also vibrate in low frequencies with long wavelengths.

### Wavelengths

Since v = fλ, where v is the velocity of sound, f is the frequency and λ (Greek letter lambda) is the wavelength, conversion of frequency to wavelength can be done with the equation:

λ = v/f

Since the speed of sound in air at room temperature is about 344 meters/second, the following chart shows the wavelengths for typical infrasonic frequencies.

Frequency (f)Wavelength (λ)
10 Hz34.4 meters
0.1 Hz3400 m
0.001 Hz344 kilometers

A wavelength of 344 km is 213.8 miles. That is a pretty long wavelength. But also 0.001 Hz = 3.6 cycles per hour. That means that each maximum of the sound wave would be about 14 minutes apart.

### Application

The primarily application of these very low frequency sound waves is in seismographs that detect and monitor earthquakes. There has been research on using infrasound as a weapon to disorientate the enemy.

Various animals, such as the elephant, whale, rhinoceros and hippopotamus, use infrasound to communicate.

## Audio frequencies

Audio frequencies are those in the range of 20 Hz to 20,000 Hz that humans can hear. Other sources give the range as 16 Hz to 16,000 Hz. The range also varies with individuals.

### Wavelengths

Wavelengths for the upper and lower limits of human hearing are calculated below. We've also included select notes or frequencies from a piano keyboard.

Piano key numberName of noteFrequency (Hz)Wavelength (meters)
----2017.2
1 (first key)A027.512.5
40C4
(middle C)
261.631.31
49A44400.79
64C6
(soprano C)
1046.50.329 (32.9 cm)
88 (last key)C84186.010.082 (8.2 cm)
----20,0000.0172 (1.72 cm)

### Applications

Anything that creates sound that you can hear is considered an application of audio frequencies. This includes your voice, radios, televisions and musical instruments.

Knowing the wavelength of a sound allows you to make a musical instrument that amplifies or resonates that sound. For example, a tube of 1/2 λ or one-half the wavelength of the sound will resonant that note or pitch when you blow across its top. That is the principle of an organ.

Thus, if you take a pop bottle with enough water in it that there is a 16.45 cm or 6.5 in column of air in it (1/2 of 32.9 cm) and blow across the top, you should hear the soprano C note of about 1046 Hz.

## Ultrasonic frequencies

Ultrasound is sound with a frequency greater than the upper limit of human hearing. This is typically above 20,000 hertz (Hz) or 20 kHz (20 kilohertz). Some industrial applications of ultrasound use frequencies up to 10 MHz or 10,000,000 Hz.

### Wavelengths

Wavelengths for ultrasonic frequencies are very small. The following table show select frequencies.

FrequencyWavelength
34.4 kHz1 cm
1000 kHz (1 MHz)0.34 mm
10 MHz0.034 mm

A sound wavelength of 0.034 millimeters is 0.0013 inches or 34 micrometers. That is a very short wavelength.

### Applications

Ultrasound is used in sonograms to produce pictures of fetuses in the human womb, as well as to show other features in soft tissues without using x-rays.

Ultrasonic cleaners are to clean jewelry, lenses, medical instruments and industrial parts. These cleaners usually use frequencies around 30 kHz.

In industry, ultrasonic frequencies in the megahertz (MHz) range are often used to find flaws in materials, as well as to measure the thickness of objects where common measurements will not do.

## Summary

Sound can be emitted and detected at a wide range of frequencies and wavelengths. Infrasound consists of very low frequency sound, beyond the range of hearing of humans. Infrasound wavelengths can reach many kilometers. Audio frequencies are those that can be heard. The piano and organ are examples of such sound sources. Ultrasound consists of very high frequencies, again beyond the human range of hearing. Wavelengths of ultrasound reach fractions of a millimeter.

Frequencies and Wavelengths of Sound - Succeed in Physical Science: School for Champions