Whistling Bottle/ Pipe
To show that natural frequencies in a pipe closed at one end is inversely proportional to the length of the pipe i.e., \(\nu\propto 1/l\).
Stationary waves are produced when two identical progressives waves (having same amplitudes, frequencies and speeds) traveling through a medium along the same path in opposite directions, interfere with each other. The points where particles amplitude is maximum are called anti-nodes and points where particles amplitude is minimum are called nodes.
one soda water bottle
Whistle through the mouth of the bottle and observe the pitch or frequency of sound. Now, fill the bottle with water to different height and repeat the whistling.
The frequency will go on increasing as you pour more and more water into the bottle. Every object has its own natural frequency of vibration. When you whistle at the mouth of the bottle, the air inside the bottle start vibrating giving out sound. It behave like a closed organ pipe. A stationary longitudinal wave is setup inside the bottle. The mouth of the bottle, which is open to the outer atmosphere has an anti-node and the closed end has a node. We know that frequency of vibrating air column in a pipe is dependent on the length of air column (for fundamental mode in a pipe closed at one end \(\nu=v/4l\)). As you pour water into the bottle, the length of air columns gradually decreases and hence frequency of the fundamental mode increases.
Take a transparent flexible pipe of 1/2 in diameter and 1 m length. Fill some water in it. Now hold one end of the pipe by one hand and another end by second hand. Bring one end close to the mouth and whistle just above it. Change the length of the air column by raising or lowering other end of the pipe. You will notice change in frequency when length of air column is varied.