Why do bells ring so long? Modes, twin modes and decay

A bell is not a single frequency

In instruments such as strings or air columns, the overtones are whole multiples of the fundamental. Bowls, bells and gongs are shells or plates: they vibrate in several shapes at once, and the frequencies of these shapes are not whole multiples of the fundamental. In Frekans Studio's singing-bowl table, the second mode sits at about 2.71 times the fundamental and the third at 5.13 times. This inharmonic series is what makes a bell sound like a bell.

The Resonance Lab draws each mode as a ring: the low mode in the centre, the high modes outside. The rings are worked out from the instrument's table of modes, not from a recording.

Why does it ring so long?

Struck metal loses energy by radiating it into the air and turning it into heat inside itself; this loss is very slow. Each mode's level falls in equal steps, exponentially. The time it takes for the sound to drop by 60 dB is called T60; the Lab's table of modes lists the T60 of each mode.

High modes usually fade sooner. So a sound that is bright and crowded right after the strike becomes simpler over time, until little more than the fundamental is left. The damping slope setting widens or narrows this difference.

Twin modes and the slow wavering

A real bowl is not perfectly round or uniform. So each mode splits into two very close frequencies. When two close frequencies sound together, their sum slowly grows stronger and weaker: this is the 'wah-wah' wavering you hear in a bowl.

In Frekans Studio the beat of twin modes is at most 2 Hz (two waverings a second). The Lab shows this beat only in text; the screen never flashes along with it.

The mallet, the strength and the gong's bloom

A soft mallet stays in contact with the instrument for longer; this long contact gives little energy to the high modes and the sound turns darker. A hard or metal mallet touches only briefly, excites the high modes too, and the sound turns brighter. A strong strike is not only louder but also a little brighter.

In a large gong the upper modes swell a moment after the strike: energy flows from the low modes to the upper ones and the gong 'blooms'. This only happens when the gong is struck hard enough; after a gentle strike the gong stays deep and plain. In the Lab you can hear the difference by changing the strike strength.

Why does rubbing make a bowl sing?

When a mallet is run around the rim of a bowl, friction gives the fundamental a little energy on every turn. As long as more energy goes in than is lost, the sound swells and then holds; when the rubbing stops, the bowl fades as if it had been struck. In the Lab, pressing and holding a bowl starts rubbing after the strike, and the sound fades when you let go.

What does the room change?

A room adds its own tail to a sound: reflections go on being heard for a while. In a stone room or a hall this tail grows longer; in a wooden room it is shorter. The instrument's own decay does not change; what changes is the space the sound is heard in.

Frequently asked questions

Why aren't a bowl's modes whole multiples of the fundamental?

A bowl is a shell; it does not vibrate in one dimension the way a string or an air column does. The frequencies of a shell's vibration shapes do not form a series of whole multiples; that is where a bell's metallic colour comes from.

Do the rings in the Lab come from a recording?

No. The rings and the table of modes are worked out from the instrument's table of modes and the moments it is struck; no audio data is used. The sound itself is generated on your device, not recorded.

Does the sound of a bell or bowl have health effects?

This article only describes the physics of the sound. What is known about singing bowls and sound baths, with an evidence summary, is in the 'Singing bowls and sound baths' article.

Listen and try

• Resonance Lab
• Sound → Silence
• What are singing bowls and sound baths?
• Gong Bath