Analogy of Sound Waves with a jump rope

(standing waves)

Take a jump rope. Raise and lower the end quickly.

The resulting pattern appears as a sign wave.

Below appears to be a full wave or 2 pi radians.

or

Now tie the end of the jump rope to an opposite point across the room, and continue raising and lowering the end quickly, at a constant frequency.

Not just any freq, adjust the freq so that a standing wave appears.

Question:

If your friend placed his/her finger at the point that appears to be a point of no movement the standing wave is not interfered.

Why? It’s actually a point of no movement.

What if your friend touches anywhere else?

Ans: The standing wave is destroyed.

Now if you want to mathematically model pressure (sound) waves, the above standing wave is analogous

Sound Waves

Resonance in an Air Column

If you have a double opened tube (most wind instruments), the mathematical pressure wave appears like this.

or

Do you see a pattern yet?

For an instrument closed at one end (open at other end)

or

or

You should see a similar pattern

For every resonance that occurs beyond the first resonance (or fundamental freq), the next resonance occurs at half a wavelength, λ / 2, beyond the first.

This is an example of the larger outer tube with the slight smaller inner tube that allows us to expand the system.