String vibration facts for kids

Vibrations, called standing waves, on a string. This shows the main sound (fundamental) and the next 5 sounds (overtones) in the harmonic series.

A vibration in a string is a type of wave. When a string vibrates, it creates a sound. If the string's length or how tight it is (its tension) is set just right, it makes a steady musical tone. This is because of something called resonance. Vibrating strings are super important for string instruments like guitars, cellos, and pianos.

How Waves Travel on a String

Imagine plucking a guitar string. A wave travels along it! The speed of this wave depends on two main things:

• How tight the string is (its tension).
• How heavy the string is for its length (its linear density).

The faster the wave travels, the higher the sound it makes. This idea was first figured out by Vincenzo Galilei way back in the late 1500s.

How String Properties Affect Sound

Once we know how fast a wave travels on a string, we can figure out the frequency of the sound it makes. Frequency is how many times a wave repeats in one second. A higher frequency means a higher pitch (a higher note).

The main sound a string makes (called the fundamental harmonic) depends on:

• The wave's speed.
• The length of the string.

Think of it like this: the length of the string is half of the wave's length for the main sound. So, we can use a simple formula to find the frequency:

Failed to parse (Missing <code>texvc</code> executable. Please see math/README to configure.): f = { 1 \over 2L } \sqrt{T \over \mu}

In this formula:

• is the frequency (how high or low the sound is).
• is the length of the vibrating part of the string.
• is the tension (how tight the string is).
• is the linear density (how heavy the string is per unit of length).

This formula tells us some important things about how strings make different sounds:

• Shorter strings make higher sounds.
• Tighter strings make higher sounds.
• Lighter strings make higher sounds.

Strings can also make other sounds called harmonics or overtones. These are higher-pitched sounds that are multiples of the main sound's frequency.

Seeing String Vibrations

It's hard to see a string vibrate because it happens so fast! But there are ways to make it look slower or even still.

Using Light Tricks

If you look at a vibrating string in front of an old CRT screen (like an old TV or computer monitor), it might look like the string is moving slowly or even standing still. This is called the stroboscopic effect. It happens because the screen's light flashes very quickly. If the string's vibration speed is close to the screen's flash speed, your eyes play a trick on you!

You can see a similar effect with a fluorescent lamp. These lamps also flicker very fast.

Using a Stroboscope

A special tool called a stroboscope can help you see string vibrations clearly. This device has a light that flashes at a controlled speed. If you match the stroboscope's flash rate to the string's vibration frequency, the string will appear to stand still. This lets you see the actual wave shape on the string!

For example, on a guitar, you can slightly change the tuning of a string to match the frequency of the electricity in your home (like 50 Hz or 60 Hz). Then, under a flickering light, the string might appear still.

Real-World String Example

Let's look at a real example with an electric guitar string. Guitar strings are designed to make specific notes when played.

A typical electric guitar has a certain distance from its nut to its bridge. This is the vibrating length of the string. Guitar strings also come in different thicknesses and are designed to be tightened to a specific tension.

By using the formula we learned earlier, we can calculate the expected sound frequency for each string. When these calculations are done, they show that the strings, when tightened to their recommended tensions, produce the standard notes of a guitar.

For example, the thinnest string on a guitar (String no. 1) is often an E note. The calculations confirm that its recommended tension and thickness will make it vibrate at about 330 Hz, which is very close to the musical note E₄. Each string on the guitar is designed this way to produce its specific note.

Images for kids

• 

  This diagram shows how we think about the forces on a small part of a vibrating string.

See also

• Fretted instruments
• Musical acoustics
• Melde's experiment
• String resonance