Changes in tension are very important when it comes to forming standing waves. This is especially true in musical instruments like guitar strings and air columns in wind instruments.

When the tension in a string goes up, the speed of the wave moving through that string also goes up. This is shown in a simple formula:

Wave Speed Formula:
( v = \sqrt{\frac{T}{\mu}} )

In this formula:

• ( v ) is the speed of the wave.
• ( T ) is the tension in the string.
• ( \mu ) is the mass per unit length of the string.

As the tension increases, the frequency of the standing wave changes too.

Key Points to Remember:

• Nodes and Antinodes:
  In a standing wave, nodes are spots that don’t move at all. Antinodes are the spots where the movement is the greatest. When you change the tension, it also changes where these points show up.

• Frequency:
  The fundamental frequency, which is the basic note or first harmonic, can be shown with this formula:

Frequency Formula:
( f = \frac{n}{2L} v )

In this formula:

• ( n ) is the harmonic number.
• ( L ) is the length of the string.
• ( v ) is the speed of the wave.

Example:

Think about a guitarist tuning their guitar. When they tighten the strings, the increased tension makes the notes higher in pitch. This creates different standing wave patterns where the nodes and antinodes move around.

This idea is used to tune all kinds of musical instruments to get the right notes.