A

# resonance

Barton's pendulum (A) provides a good illustration of mechanical resonance. A number of pendulums of varying lengths are suspended from a string. When a weighted pendulum oscillates, all the pendulums will begin to swing. The amplitude of their swing depends directly on the length of the string to which they are attached. A pendulum with the same length of string as the initial weighted pendulum, and hence the same natural frequency, will swing with the greatest amplitude.

An external force acting periodically at the resonant frequency may be used to produce resonance. A repeated thrust on one end of a diving board (B), enabling it to store up energy, will give an increasing amplitude of oscillation. A liquid in a U-shaped tube (C) can be set in oscillation by blowing in the end of the tube, but the size of oscillations are limited by friction with the walls.

A wind instrument's effective resonant length is changed by unstopping a hole.

If two strings are tuned to the same note (i.e., tuned so that their natural frequencies are the same), and one is plucked the other vibrates as well. The sound waves cause a sympathetic vibration.

Clarinet with all holes stopped (top) and all closed (bottom).

Resonance is the enormous increase in the strength of a vibration that occurs when the frequency of an applied force happens to equal the natural frequency of an object. Every object has natural frequencies of vibration. In other words, if an object is allowed to vibrate freely it makes a definite number of vibrations each second. An object can be made to vibrate at almost any frequency we wish by applying forces to it at regular intervals ("forced vibrations") but the strength will be small – except when resonance occurs.

The principle of resonance is important in music. A guitar, a piano, a trombone, in fact any instrument, is built so that it will resound with the notes played on it. This resonance makes certain of the notes and their harmonics louder than others, and this is what largely gives the instrument its characteristic tonal quality. Thus a clarinet does not make quite the same sound as a bassoon, even where both instruments are playing the same note.

## Sound and vibrations

Everything that makes a sound is vibrating. The tolling of a bell is simply the vibration of the metals hell when it is struck by the clapper. The vibrating shell pushes and pulls the surrounding air which in turn pushes and pulls the air beyond. In this way the vibrations of the bell are transmitted through the air to our ears where they are picked up as sounds. The pitch of any sound is decided by how fast the air is shaken. The lower the frequency of vibration the lower the note and the higher the frequency the higher the note. You can't hear a swinging pendulum nor a dog-whistle because some notes (frequencies) are too low and others too high for the human ear to detect.

## Natural frequency and forced vibrations

Every object has a natural frequency of vibration. In other words, if an object is allowed to vibrate freely it will make a definite number of vibrations each second. An object can be made to vibrate at almost any rate we wish by applying forces to it at regular intervals (this is called forced vibration) but the amplitude (strength) of the vibrations will be small. Resonance is the enormous increase in the size of the vibration that occurs when the frequency of the applied force happens to equal the natural frequency of the object.

A suspension bridge, for instance, has a natural frequency of vibration depending upon a number of factors such as its size, method of construction, and the materials from which it is built. This is why a company of soldiers crossing such a bridge is ordered to break step; there is just a slight chance that the frequency of the marching steps might equal the natural (resonant) frequency of the bridge and cause vibration to build up to a dangerous extent. It has been known for gusts of wind to strike an apparently sound bridge at a rate equal to its natural frequency and for swaying to build up until the whole structure has collapsed. In a similar way wine glasses can be shattered by the singing of high notes. Again the explanation is that the glass vibrated vigorously in sympathy with sounds whose frequencies are the same as the natural frequency of the glass. Waves of compressed air (sound waves) striking the glass at the same rate as its natural frequency cause resonance and the glass literally shakes itself to pieces.

## Musical instruments and resonance

Musical instruments depend upon the fact that every stretched string, every pipe, diaphragm or reed has its own natural vibration frequency. When set in motion each will send out vibrations of its own frequency into the surrounding air. If a guitar string is kept at constant tension it will vibrate at the same rate every time it is plucked. In other words, the note produced will always be the same, since the pitch of the sound depends upon the frequency of vibration. An organ pipe will always produce the same note too. When a jet of air strikes the sharp edge of the pipe it vibrates at many different frequencies but only one of these, equal to the natural frequency of the pipe, will cause the air in the pipe to vibrate any considerable amount and produce a loud note, i.e. will cause resonance.

The natural (or resonant) frequency of a pipe can be altered if the length of the vibrating column of air in the pipe is changed. In other words the pitch of the sound or note it produces can be altered in this way. The shorter the length of the air that is allowed to vibrate the higher the frequency of vibration and hence the higher the note. The longer the length that is allowed to vibrate the lower the frequency and the lower the note. The slide of a trombone, for instance, alters the resonant length of the pipe, i.e. the length of the column of air that is allowed to vibrate (in sympathy with one of the many forced vibrations set up by players' lips) and thus alters the note it is heard to play.