Los Senderos Studio
Frequency, wavelength, and amplitude
 Issue 64 January 2015 
Soundwaves

Words from the Glossary

Last month we took a look at phase. However, we probably should have discussed some other properties of waves first. So this month we will look at frequency, wavelength, and amplitude.

Frequency, wavelength, and amplitude

This month's terms: frequency, wavelength, amplitude, hertz (Hz), kilohertz, cycles per second, resonant frequency, standing wave, wave velocity, speed of sound, beat frequency, wave.
(Note: Click on the term to view its definition in the glossary.)


First, let's look at what a wave is. It is the up and down fluctuation of anything over time. That includes soundwaves, alternating current electricity, and ocean waves.

Frequency
Frequency

Frequency is how fast a wave goes up and down. More specifically, it is the number of cycles per second of a wave and it is measured in Hertz (Hz). Hertz is the unit for cycles per second and was named after Heinrich Rudolf Hertz, the scientist who first proved the existence of electromagnetic waves, not the guy who started the rent-a-car company. A cycle is one complete passage of a wave from crest to crest or trough to trough. Kilohertz (kHz) is 1,000 Hertz or 1,000 cycles per second. Frequency of sound is perceived by the human ear as notes or tones, just as frequency of light is perceived by the human eye as color. For example, middle C has a frequency of approximately 261 Hz.

Amplitude
Amplitude

Amplitude is the amount that a wave changes. It is the height of the wave as measured from an imaginary center line to its peak. The human ear perceives amplitude of sound waves as loudness.

Wavelength
Wavelength

Wavelength is the length of one wave cycle. Wavelength is related to frequency according to the formula velocity equals frequency times wavelength.

So why would this information be important in a recording studio. Well, in some circumstances with the right conditions, you can set up a standing wave. We'll get into standing waves in more detail next month, but a standing wave is one that begins and ends right on a surface, such as a wall. It is like two people swinging a jump rope, except where their hands should be is a wall. The problem with a standing wave is that its amplitude (and, therefore, it's loudness) depends on where you are in a room. Near the center of a room it would be very loud, but at the walls nearly silent. This obviously would not be good for a recording studio.

A standing wave occurs when its wavelength equals the distance between the two walls. For example, low C has a frequency of 130.81. Let's use the formula above to calculate the wavelength. For velocity, we will use the speed of sound. (Velocity and speed are the same for our purposes, but if you are a scientist, velocity indicates speed and direction, while speed has no direction.) Unfortunately, the speed of sound varies with temperature and humidity. See the table on our website. At 43 degress and 40% relative humidity, the speed is 1100.3 feet per second. In a typical recording studio, the speed of sound is probably a bit higher than that, but most people round it off to 1100 feet per second. So the wavelength of low C would be 1100 divided by 130.81 or 8.4 feet. So if you were in a room where the walls were 8.4 feet apart and your bass player plucked a low C, he would set up a standing wave. But wait . . . that's not all, every C above that on the musical scale would also set up a standing wave. We'll delve into that statement a bit more next month.

Another problem you might encounter is resonant frequencies. A resonant frequency (also called natural frequency) is the frequency at which an object tends to vibrate with a greater intensity than at other frequencies. Every object has a resonant frequency, but it may or may not be within an audible frequency range. You may notice a resonant frequency when your table on which your television sits begins to buzz when the soundtrack on the TV starts playing some really low notes. This phenomenon is a problem that designer of loudspeakers, microphones, and other audio equipment are well aware of. They take great pains to design their gear in a way that resonsnces do not occur audibly. In the studio, you may not be so fortunate. Sometimes when the guitar player plays really loud, other things begin to vibrate, such as snare drums, high hats, and cymbals. Usually the only solution is to isolate the offending object.

Another example would be recording a guitar with two microphones. If the distance between the two microphones is one-half wavelength of a particular tone, then the signal of that tone received by the first microphone will be 180 degrees out of phase with the signal from the second mic. When combined, the two signals will cancel one another. Because a guitar plays more than one note, some notes will be increased while others will be decreased. A plot of such a recording will show peaks and troughs in intensity, which is called a comb filter, because the peaks and troughs resemble the teeth in a comb. Such as recording is said to be phasey as the sounds seem to come from no particular direction.

One way to correct the problem is by using the 3 to 1 rule. It says when two microphones are used to record a source, the second microphone should be placed at three times the distance from the first mic as the first mic is from the sound source. But it is only a rule of thumb and sometimes that does not work. Another solution is to reverse the polarity of one of the signals. This can be effective, particularly on something like miking the top and bottom of a snare drum. For this reason, many consoles and digital audio workstations have a button marked "phase inversion" or "phase reversal." However, that is a misnomer as what it really does is change the polarity, not the phase. It should be marked "polarity inversion" or "polarity reversal." When the phase difference remains constant over a given time period, it said to be phase coherent.

Another problem sometimes encountered in the studio is phase distortion, which sometimes occurs when a plug-in or effects processor causes the phase of the signal to shift. To avoid this problem, one should seek out software and hardware that is phase linear, the ability to process an audio signal without causing any phase shift.

The last term we want to visit this month is beat frequency. A beat frequency is the frequency of a sound wave created by the combination of two sound waves of similar but slightly different frequencies. The beat frequency is the difference between the frequency of the two waves beating together. Before the days of electronic tuners, musicians would often use the beat frequency to tune their instrument. Using a reference tone such as on a piano, the two notes are sounded simultaneously. When the instrument is way out of tune, rapid beating occurs. As the two notes near one another, the beating become slower and slower until it disappears. The two instruments are now tuned to the same note.

Next month we will take a look at standing waves.

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