Science of sound in a flute

Himanshu Nanda Author

Posted On Jul 18, 2023 |

Bamboo whispers physics secrets! Dive into "Science of Sound" & unlock the science behind its melodic magic. Learn air, physics, & flute mastery!

Bansuri is one of the most melodious instruments there is. It is hard to believe that a simple bamboo can be transformed into a brilliant instrument that produces the most magical sound. We will look into the science behind the sounds the humble flute produces in this article.

How Sound Travels Through the Air

We have been learning about how sound travels through air since our school days. Let’s do a quick refresher. When sound is produced, let’s say by beating a drum, the air particles that are next to the source of sound vibrate. This vibration is transmitted to particles that are next to them and so on. This movement, that allows sound to travel through air quickly, is called wave compression as depicted in Fig. 1.

Fig. 1. A sound vibration travelling from a source to our ears.

How our ear hears the sound through these wave compressions is fascinating too. These sound waves first hit the outer ear. Our ear is shaped in a way that can carry the sound waves in a concentrated manner to the inner ear, just like a funnel.

The sound travels from the outer tear passing through the ear canal and finally hits the eardrum. The eardrum, in turn, vibrates and passes the signals to the middle ear. The middle ear is made of 3 small bones that receive these signals and amplify them.

These amplified sound signals are then sent to the inner ear which is filled with fluid. A lot of complex tasks transmit the sound from here to the auditory nerve that finally sends the sound to the brain.

All of this happens almost real time. Now how music is created, transmitted through air and finally gets processed in our brain.

Basic Characteristics of a Sound Wave

A wave is an oscillation (disturbance) that travels through space and matter. A sound is an example of a wave traveling through air molecules to our ears. The sound travels as fast as 1,225 km/h in air at 150C! However, if bansuri is played in vacuum, there will be no sound.

The basic characteristics of a wave are: the wavelength (λ), the frequency (ν), and the speed (c). The number of vibrations of a wave in one second is termed as the frequency. The wavelength is the distance on which a wave repeats as shown in Figure 2.

The relation between them is as follows:

Frequency(ν) = Speed (c) / Wavelength (λ).

Fig.2. The characteristics of a travelling simple sinusoidal wave.

In music, the frequency accounts for the sharpness or pitch of a sound. For example, the musical notes of the upper octave of a bansuri have higher frequencies than the lower octave.

The model of physics for bansuri: Open Organ Pipe

There are different models in physics that can explain how different musical instruments like flute, harmonium, or drums, create musical sound. For example, a transverse flute or a bansuri works on the principle of an open organ pipe since it is open at both ends, (i.e., at the mouth hole and at the other end).

An organ pipe is a musical instrument that creates different frequencies sound, when the air is blown through it. When a bansuri is played (as you can see in the free Flute lesson online), these vibrations are created. They travel from the other end in space and spread through air. The figure below depicts the wave patterns in an open organ pipe or bansuri, i.e., different modes of vibration.

Fig.3. The waves are created in an open organ pipe or a bansuri:

a) In the fundamental mode, b) In the 1st overtone. For example, when we blow softly a bansuri with all holes closed, it will create the sound of PA(lower octave), or the waves in the fundamental mode (XX-link to free online bansuri lesson). But when we blow stronger, it will give PA(middle octave), or waves in the 1st overtone, with half of the wavelength.

In the fundamental mode, or when we blow softly a bansuri, we have the following relation between frequency (ν1) and air column length, L.

ν1 = v / λ1 = v / 2*L.

In other words, changing the length of the air column would change the frequency of the wave. Based on this principle, the different musical notes, or the sound waves of different frequencies are created in a bansuri.

For example, in a bansuri, a Sa is played by closing the first three notes and a Ga is played by closing the 1st hole, as shown in the free flute lesson online (fig. 4). The respective lengths of the air columns would be LSa and LGa, with a νSa = v / λSa = v / 2*LSa and νGa = v / 2*LGa. Therefore, νSa / νGa = LGa /LSa. As an example, For a typical A scale flute, where the frequencies of Sa and Ga are, νSa = 440 Hz and νGa = 554.4 Hz, respectively. This will lead to LGa /LSa = 440/554.4.

Fig.4. The air columns showed for the notes Sa and Ga in a bansuri: For a typical A scale flute, where the frequencies of Sa and Ga are, νSa = 440 Hz and νGa = 554.4 Hz, respectively. This will lead to LGa /LSa = νSa / νGa = 440/554.4.

On the basis of this principle, a flute maker creates holes for different notes while making a bansuri. These holes are closed and opened in a particular way to produce the sounds of a musical octave, as is shown in the free flute lessons online.

To produce overtones, or frequencies multiples of the fundamental frequency, the bansuri is needed to be blown strongly, as is shown in the free online flute lesson. Figure 3 b) Shows the mode of vibration for 1st overtone, for example, for Sa of higher octave:

where λ2 = L or ν2 = v / λ2 That implies, ν2 = 2* ν1

ν1 being the frequency in the fundamental mode, for Sa of middle octave.

The frequency of the first overtone is double of the fundamental frequency. As an example, we see the A scale bansuri in the figure 5. It has a fundamental frequency of 440 Hz and the mentioned length is 39.2 cm for the air column of playing a Sa (shown in Figure 5). When I take this flute and blow it softly with three holes closed(shown with Red filling), then it will blow at a Frequency of 440 Hz which is Sa. But if I blow it more powerfully, then it will blow in 1st overtone with a frequency of 880 Hz which is the Sa of upper octave, as explained in Free Flute lesson online.

Fig.5. An A scale flute showing the fundamental mode.

On the same principle, one could calculate the corresponding length of the organ for a particular frequency, or different musical notes. As an example, table 1 shows the length required for producing different musical notes in an A scale bansuri. This table can be used for drawing holes while making an A scale bansuri.

Table 1. The frequency table that can be used for drawing holes on making an A scale bansuri.

Conclusion

A bansuri works on the principle of an open organ pipe as described above. The blowing air pressure is used to create higher overtones or the notes of higher octave while the finger holes are used to create different notes of a musical octave (free online bansuri lesson). The distance of the finger holes are calculated from the length derived from the frequencies of a musical octave. In other words, the seven musical notes correspond to seven different frequencies, based on one base frequency to which a bansuri is tuned.

The same principle can be extended to create different scales of bansuris. The different scale bansuris are set in tune to different base frequencies and accordingly holes are placed and made, depending on the length and diameter of the bamboo.

We welcome you to look at the free online bansuri lesson on themysticbamboo.com where you can explore how this magical instrument creates a musical octave.