The Physics of Singing

Sound is just sound — no matter who or what is producing it — and so the rules of singing really do just follow the rules of physics. In this blog post, I’ll focus on how sound waves work in both the universe and our bodies to create amazingly spectacular sounds. It’s a big read, so be ready!

SOUND WAVES:

Sound waves are generated by a sound source. Once the source is activated, the energy created by that source repeats over and over again – in the form of waves – as it moves through what’s called the medium (“stuff” such as air or water). As that energy moves through that medium, it vibrates the particles inside of the medium. You can visualize it like a pebble being dropped in a lake.

For example, think about how you can feel (vibrations) the booming low bass notes (energy) of a song in your body (medium) when you turn on the radio (source).

In singing, the sound wave source are the vocal cord vibrations, the energy is the note, and the mediumis your body (and it also extends to anything in the vicinity.)

FREQUENCY: The frequency of a pitch/sound refers to how often the particles of the medium vibrate when a sound wave passes through the medium. Put another way, the frequency is how quickly the sound wave repeats itself over and over again in the medium. (For example, put your fingers on your nose and humm a high note —  you’ll feel the vibrations coming through your nose more often (feels like faster) than if you hummed a low note).

Measurements: Frequency is measured in cycles per unit of time called Hertz (Hz). 1 Hz is equal to 1 cycle (repetition of the wave) per second). Middle C has a frequency of about 262 Hz. This means that each second, to make a Middle C, your cords are vibrating 262 per second, and each one of those vibrations is creating a wave of energy that is then sent out into the world at that speed. In general, men's vocal folds can vibrate from 90 - 500 Hz, and they average about 115 Hz in conversation. Women's vocal folds can vibrate from 150 -1000 Hz, and they average about 200 Hz in conversation. Here is a handy list of pitch frequencies: http://www.phy.mtu.edu/~suits/notefreqs.html

INTENSITY: Besides frequency, intensity is the other important aspect of a sound wave. Intensity is how much energy is being carried in the sound wave. The greater the amplitude (the largeness) of vibrations of the particles of the medium, the greater the rate at which energy is transported through it, and the more intense the sound wave is. In other words, if the particles in the medium vibrate in a big way when the sound wave hits them, then the intensity is high; if they only vibrate a little, then the intensity is low.

Intensity (in sound) can be roughly defined as volume. The higher the intensity, the louder the note is.

(This is mostly true. Because of the human ear's tendency to amplify higher range frequencies (1000 Hz to 5000 Hz), high notes will seem louder to the human ear than low notes, even if sung at the same intensity. Also, it should be noted that the intensity also gets less the farther the sound wave travels – for example, you sound quieter to standing someone far away, even though your original volume was the same as what the person standing closer to you heard.)

Measurements: While officially we measure intensity in Watts/meter (how much energy is contained in the sound wave per every meter it travels), decibels (dB) is the most common way to rate volume/intensity. (The threshold of hearing is assigned a sound level of 0 dB; this sound corresponds to an intensity of 1*10-12 W/m2.) Rustling leaves are about 10 db; very loud music in headphones is 100 db, and your eardrum will pop at 160 dB.

QUICK NOTE ON THE DIFFERENCE BETWEEN FREQUENCY AND INTENSITY: Frequency is how often the sound wave repeats; intensity is how much energy is contained within the sound wave. So, if I sing Middle C softly, that sound has a lower INTENSITY but the same FREQUENCY as if I sang a Middle C loudly. Conversely, I could have the same volume when I sing a Middle C or a Middle G at 30 dB – and though their INTENSITY would be the same, their FREQUENCY would be different.

HARMONICS

When a sound wave interacts with a medium/object, it’s important to remember that the medium/object has its own tuning (or tendencies), and so will tend to vibrate more at one particular frequency (or a set of frequencies). The frequency or frequencies at which an object tends to vibrate with when hit, struck, plucked, strummed or somehow disturbed is known as the natural frequency of the object. (This is how singers break glass. They sing at the natural frequency of the glass at such an intensity to vibrate the particles in it enough to break it.)

Natural frequencies of objects are also how harmonics are created. Harmonics are created by the interaction of fundamental sound wave (pitch) with the natural frequencies of the object it is moving through. When you sing, we not only hear the original vibration (pitch), we also hear the harmonics that are created through the interaction of the sound wave frequency and the natural frequencies of your vocal resonance chambers (the areas of your head, cheekbones, nose, sinuses, and more). This gives the sound beauty and interest.

A silly example is that if you say a sentence (a sound wave frequency) to a nice person (object’s natural frequency), they will hear it as a kind statement (resulting harmonics); but if you say the same sentence (a sound wave frequency) to a mean person (a different object’s natural frequency), they will hear it as an insulting statement (different resulting harmonies).

Measurements: Our language on describing this is a little convoluted. The pitch (frequency) of a note is sometimes called the fundamental. The 1st Harmonic of a sound is this fundamental (pitch). The rest of the harmonics go up from there. The 2nd harmonic is usually an octave up, and 3rd Harmonics is a musical fifth above that. Sometimes the word overtone is used. The 1st Overtone is the same as the 2nd Harmonic – don’t get confused! Here’s a link to example of what the first 16 overtones/harmonics sound like: https://en.wikipedia.org/wiki/Overtone.

TIMBRE: In music, timbre (tam-bər) is also known as tone color or tone quality. Different types of sound-producers, such as different people’s voices or different instruments, sound different even when they are singing/playing the same note. This difference is what’s known as timbre. Timbre is the result of harmonics and intensity/volume (sometimes talked about together as the spectral envelope.)

SPECIFIC LANGUAGE USED IN VOCAL STUDY TO DISCUSS THE PHYSICS OF SINGING

Just like any field, vocal technique has its own words and jargon.

RESONANCE: In singing, resonance refers to how the sound is “shaped” by the sound wave moving through the spaces (mediums) of your throat, face, and head. As singers, we modify the size and shape of these mediums (a.k.a. “resonators”; a.k.a. “resonance chambers”) to amplify their best natural frequencies so as to create great harmonics…and a great sound. Some examples of changing the shape of a medium would be lifting your soft palate or dropping your jaw.

FORMANTS: As you now know, the sound wave frequencies that most ‘jive” with the natural frequencies of an object will themselves increase in amplitude (a.k.a. volume). So, as the sound wave goes through each of your resonance chambers (throat, face, head), each one will increase the amplitude of a certain frequency or set of frequencies. In singing, these highlighted frequencies are called formants.

Silly example: You meet someone, and their love of pets really “resonates” with you – you both strongly share that love. So, when you are hanging out, you do lots of pet-related things because the love of pets becomes stronger when you are together (it is amplified). So, in this example, the love you have for pets is the sound wave frequency. The love your friend has for pets in the natural frequency of the resonating chamber. The increased love of pets when you are together is the formant.

There are lots of formants, as there are lots of parts of you, but here are the four that get talked about the most in singing:

The 1st Formant is the highlighted sound that results from the interaction of the sound wave (that you created with your vocal cords) — called the fundamental pitch — with the positioning of the jaw. The more your jaw is dropped, the higher the highlighted frequency of the 1st Formant. The 1st Formant is generally around 500Hz (+/-300).

This is important for singing. If the fundamental/pitch is low (let’s say it’s the note G2 with a frequency of 100 Hz) and the 1st Formant pretty normal (say, 500)), you’ll get a number combination (100 and 500) that creates a rich and lovely sound.

But, what if the fundamental number is close to the 1st Formant number? Let’s say the fundamental is a C5 (with frequency of 400) and the 1st Formant is at the normal 500 Hz. In this case, the resulting sound will be thin and strident because the numbers are too close together to make an interesting sound.

So, when singing a note with a high fundamental number (like C5 and above), it’s important to really drop your jaw — so as to increase the number of the highlighted frequency of the 1st Formant (to like, say, 800). That way, instead of the thin 400-and-500 combination, you’d have a rich-sounding 500-and-800 combination!

The 2nd Formant is the highlighted sound resulting from the interaction of the sound wave with the positioning of the tongue. A higher arched tongue creates a higher highlighted frequency in the 2nd Formant. The 2nd Formant lives around 1500Hz (+/-800).

Remember, now, that our ears highlight frequencies between 1000 and 5000 Hz, so by arching our tongue, we can highlight the 2nd Formant and make it easier for the audience to hear lower pitches.

Also, the 2nd Formant is crucial in creating the musical theatre sound in particular. Sound spectrums (visual representations of sound) show the strongest peaks in the 2nd Formant range when singing musical theatre. So, arch your tongues in this style!

The 3rd Formant is the highlighted sound resulting fom rounded lips vs unrounded lips and the tip of the tongue position. The 3rd Formant is around 2500 Hz.

(The 4th and 5th formants are determined by vocal tract length, pharynx shape, and larynx shape. Not gonna talk about those.)

SINGER’S FORMANT: Singers do something cool while singing well — they actually create another formant…one that doesn’t exist in speech! It is right around 3000-4000 Hz, and creates the “ring” that people associate with great singing. By widening the pharynx and lowering larynx, singers create a new little resonator shape that highlights frequencies in the 3000-4000 Hz range – which is delightful because it matches the frequencies that our ears like to highlight. The result is a sparkly, shimmery sound specific to only the human voice.

FUN FACT TO END ON:

Intervals that we hear as pleasing to the ear have really “clean” numerical relations to each other! That’s one reason singing exactly on pitch is crucial…

Interval Frequency Ratio Examples:

Octave — 2:1 (for example, 220 Hz and 440 Hz)

Third — 5:4

Fourth — 4:3

Fifth — 3:2

Great job! You got to the end!