Basics of Wave: String Waves

Basics of String Waves

The other day, talked about the speed of the waves to find the tension of the strings.

To know more about the speed of the wave of a string,
first I will summarize the basics of waves.

String Wave : Standing Wave

A string wave with both ends fixed is consisted from large vibration parts (arc) and non-vibrating parts (node).

pink = arc
gray = node

Such waves are called standing waves.

Wavelength

Only one wave, (for example)

0. From the original point..
1. Goes up..
2. Back to the original point..
3. Goes down..
4. Return to the original point.

The length of this wave is the wavelength λ.

Wave frequency and periodic Time

The periodic time of the wave T [s] is the time it takes for a wave to undulate once.
If there is one wave per second, the cycle is 1 second.
If there are two waves per second, the cycle is 0.5 second.

Wave frequency f [Hz] is the number of waves per second.
One wave per second is 1 [Hz].
2 waves per second is 2 [Hz].

The frequency f per second is

The periodic time is

String Length and Normal Vibration

The normal vibration is the vibration between the closest adjacent nodes of the wave. (ex. gray to gray)

In reality, the strings have overlapped by various waves.

Waves of many frequencies are combined.

For the smallest wave (natural node n = 1), the length of the normal vibration is the length of the string.

The length of the string with wavelength λ1 (normal vibration) is L = 1/2 λ1
The length of the string with wavelength λ2 (double vibration) is L = 1/2 λ2
The length of the string with wavelength λ3 (3x vibration) is L = 1/2 λ3
Wavelength λx followed by ...

The length of the string when considering the resonating frequency n is

When the wavelength of the normal vibration is λ1 (normal vibration), the length of the string is λ1 = 2 L.

Summary

- The vibration wave of the string becomes standing waves
- The wavelength λ is the length of one wave
- The periodic time T of the wave is the time when the wave undulates once.
- The frequency f of the wave is the number of times it undulates per second
- The normal vibration is between the adjacent nodes closest to the wave.
- The length of the normal vibration with natural node n = 1 becomes the length of the string.