The Sound of Bells

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Bell sounds and time

The sound a bell makes is initially loud, and decays away over time. Here is the bell used by Perrin and Charnley in their research. The bell was sounded with a gentle tap from the clapper and then allowed to vibrate freely.

Plot of bell waveform

About 12 seconds of sound are shown. The waviness is caused by doublets.

Apart from the beating from the doublets, the sound decays steadily from a maximum to quietness. But when we look at the variation over time of individual partials, a completely different picture emerges. Here are the amplitudes of some of the main partials from this recording plotted against time.

Time profile of main partials - Perrin and Charnley bell

The partials show markedly different behaviour. The hum starts at low intensity, and grows to a peak over several seconds before starting to fall again. The prime starts at a high amplitude, falls a little, rises again and falls away slowly, with a few wobbles on the way. This partial is a doublet, with spacing about 1Hz. The tierce shows a similar profile to the prime, but decays a little slower. The nominal drops extremely rapidly from an initial high intensity. The profile of the other partials is harder to see because of their lower intensity, but plotted on a different scale would show further differences in profile.

When a clapper hits a bell, the effect is dramatic and immediate. Many modes of vibration are stimulated, some of them very short lived. Energy passes between the various modes of vibration, some increasing in amplitude, some decreasing. After a while, the bell settles down to a more settled mode of vibration with partials slowly dying away. The effect is similar to that of throwing a stone in a pond – a big splash, followed by ripples that run across the surface of the water for quite a while. The sound of a bell can be divided into the ‘splash’, the major disruption as the clapper hits and shortly after, and the ‘tail’, during which time the intensity of the partials falls slowly to zero.

There is no better way to demonstrate this than by playing a bell sound backwards – first demonstrated in a radio program by Albert Hughes of the Whitechapel bellfoundry. Here is taylor.wav backwards. The sound of the bell slowly grows, sounding brighter and brighter (caused by the amplitude of the high frequency partials increasing) until it ends in a brief sibilant rasp.

Taylor backwards

The rate at which the partials decay is different in different bells. The bellfounders suggest that uncut or maiden bells, and bells with a poor metallic composition, have partials which decay more quickly, producing a deader sound. Here is a bell from the York foundry, cast about 1500. Note how quickly all the partials die away, giving a much drier sound compared with the previous bell.

Time profile of main partials - Brompton bell

When a bell is rung full circle, the clapper hits the bell hard, may bounce one or more times, and then lies against the bell, damping certain vibrations. The plots below show the amplitude of key partials over time for a bell, both struck when down, and rung full circle. Unfortunately, the bell has doubleted partials, which oscillate up and down even in the sound from a single clapper stroke. Here's the bell chimed when down:

Ranmore tenor - chimed while down

and here it is rung full circle:

Ranmore tenor - rung up

The slower initial risetime of the partials in the second plot is due to the recording having been taken from the ringing room rather than the bell chamber. Due to the doublets, it is not really possible to see the clapper bounce - though one can imagine that the multiple peaks in the nominal in the second plot might be indicative. It is clear that after about a second or so, the vibration of the bell in the second case is being damped by the clapper lying on the bell, though the tierce seems to be holding up best. Comparing the two graphs, it is re-assuring that the same set of partials seem to be important in both cases - the nominal, superquint, tierce, octave nominal etc. The octave nominal is less prominent with the bell rung up, whether this is due to the clapper bounce or the sound coming through two floors is not clear.

Here is a plot of partial intensity and position for the two cases - up and down. The transform was done over one second.

Ranmore tenor - transforms up and down

The increased prominence of the tierce and superquint and the reduced prominence of the octave nominal and higher partials can be seen.


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Last updated September 21, 2000. Site created by Bill Hibbert, Great Bookham, Surrey