Question

What is the first harmonic?

Answer 1

Hint: There are two types of tubes. One is, the tube with 2 open ends and the other one is, the tube with 1 open and 1 closed-end. In the case of the tube with 2 open ends, the first harmonic will have 2 antinodes and a node, whereas, in the case of the tube with 1 open end and 1 closed-end, the first harmonic will have 1 antinode and a node.

Complete answer:
The first harmonic is also called the fundamental frequency. It is the lowest possible value of the frequency. In simple words, a wave that has only 2 nodes and an antinode is called the first harmonic. To form a standing wave pattern, the minimum possible frequency at which the string would vibrate is called the fundamental frequency.
The length of the string is given as follows.
\[L=\dfrac{1}{2}\lambda \]
Where \[\lambda \]is the wavelength of the string vibration (wave).
The frequency of the first harmonic is given as follows.
\[{{f}_{1}}=\dfrac{v}{2L}\]
Where \[v\]is the speed of the wave and L is the length of the string.
The properties of the first harmonic are:
Only half of the wave will be present in the first harmonic.
The value of half the wavelength of the string vibration (wave).is equal to the distance between the antinodes of the first harmonic.
Again, in the case of the first harmonic, the length of the air is equal to half the value of the wavelength of the string vibration (wave).
\[\therefore \]The first harmonic is the fundamental frequency, that is, the minimum possible frequency at which the string would vibrate to form a standing wave..

Note:
There are further levels of the harmonic, such as second harmonic, third harmonic, fourth harmonic and so on. The lengths of these harmonics are equal to the integral multiple of the wavelength of the vibration/wave.