You press a guitar string down at the middle of the fretboard. What happens to the note?

The vibrating part of the string becomes shorter. A shorter string vibrates at a higher frequency. The note becomes higher

What two conditions must hold for a glass to be shattered by sound?

The frequency of the sound must match the natural frequency of the glass. The sound must be loud and sustained enough to keep feeding energy in. A frequency match and a continuous supply of energy

Why are soldiers told to break step when crossing a bridge?

Marching in step is a rhythmic push at a single frequency. If it coincides with the bridge's natural frequency, resonance builds. The amplitude would grow with every step. To prevent resonance from growing the oscillations to a dangerous size

Waves and Sound · Grade 9

Why is a guitar string loud over a wooden box and almost silent without one?

Because the string on its own pushes very little air. It passes its vibration through the bridge to the body of the guitar, and that wide panel moves a far larger area of air at the same frequency. The box adds no energy — it only delivers the energy to the air more efficiently, which is why the note is louder and dies away faster.

Learning objectives

Define natural frequency and state what has to be true for resonance to occur
Explain why a guitar string sounds much louder over a wooden box than stretched on its own
Predict how the pitch of a string changes when it is shortened, tightened or made thicker
Give one example where resonance is useful and one where it is dangerous

Natural frequency

Every object has frequencies at which it will vibrate of its own accord once you give it a single push. These are its natural frequencies, and they are fixed by its size, its shape, its material and its tension.

A swing is the simplest case. It has one natural rhythm, and if you push exactly in time with it — once per swing, at exactly the right moment — it goes higher and higher from a series of small pushes.

That is all resonance is: when the driving frequency matches the natural frequency, every push adds energy instead of fighting the motion already there, and the amplitude keeps growing.

The sound box

A stretched string on its own is almost inaudible. It is thin, so it displaces a tiny volume of air, and most of the energy stays in the string instead of reaching the room.

The body solves this. The vibration passes from the string through the bridge to the broad wooden panel, which vibrates at the same frequency and moves a far greater area of air. The sound becomes much louder.

There is no free energy here. The same energy simply reaches the air faster, which is why a guitar note dies away sooner than a bare string would — more loudness over a shorter time.

Useful and dangerous

A string's pitch rises when you shorten it — which is what pressing a fret does. It rises when you tighten it, which is what the tuning peg does. And it falls when the string is thicker or heavier.

Resonance is useful everywhere: musical instruments, a microwave tuned to a frequency that drives water molecules, medical MRI, and radio tuning, where a circuit is brought into resonance with the one station you want.

It is dangerous in equal measure. A singer holding exactly a glass's natural frequency can drive the amplitude until it shatters, and soldiers are ordered to break step on a bridge so that the marching rhythm cannot resonate with it. Engineers calculate the natural frequencies of structures before building them for precisely this reason.

Worked examples

You press a guitar string down at the middle of the fretboard. What happens to the note?
1. The vibrating part of the string becomes shorter
2. A shorter string vibrates at a higher frequency
Answer: The note becomes higher
What two conditions must hold for a glass to be shattered by sound?
1. The frequency of the sound must match the natural frequency of the glass
2. The sound must be loud and sustained enough to keep feeding energy in
Answer: A frequency match and a continuous supply of energy
Why are soldiers told to break step when crossing a bridge?
1. Marching in step is a rhythmic push at a single frequency
2. If it coincides with the bridge's natural frequency, resonance builds
3. The amplitude would grow with every step
Answer: To prevent resonance from growing the oscillations to a dangerous size

Common mistakes

Thinking the sound box creates energy: It only transfers the energy already in the string to the air more efficiently. The proof is that the note dies away faster, not more slowly.
Assuming any sufficiently loud sound will break a glass: Without a frequency match there is no resonance. A loud sound at the wrong frequency rattles the glass and nothing more; only the exact natural frequency accumulates into a destructive amplitude.
Confusing tightening a string with thickening it: Tightening raises the frequency and thickening lowers it. That is why the thick strings on a guitar are the low ones, and why tuning is done by changing tension rather than by changing string.

What to remember

Resonance: driving frequency equals natural frequency.
The body improves transfer to the air, not the energy.
Short or tight = high; thick = low.
The same effect builds instruments and brings down bridges.