Finding Fundamental Length

Now we will proceed to find the Fundamental Lenth, i.e., Theoritical length

Note that this is a length from the Blowhole center to the open end. First we have to find the wave length for the fundamental, for that the equation is

C = Y x F

                       Where, C = Velocity of the sound
                                   Y= Wavelength
                                   F = frequency

Suppose i want to make the A flute with frequency = 440 Hz . The Lowest Frequency will be Pa (G), frequecny = 440x2/3= 293 Hz

So the wavelength is Y = C/F

Taking the velocity of the sound =330 m/s

Y = 330/293

Y=1.12 Mtrs

Now this is the wavelength of our first harmonics,
To find length L = Y/4
So this will be 1.12/4 =  0.28 mtrs = 28 cms.
 so the distance from blowhole to end of the other flute will be 28 cms, not considering the corrections.
Hence the length will be kept slight more to do practical tuning and finding K1 and K2, which is explained in the earlier posts.

Velocity Of Sound

Now our aim is to find the fundamental length of the Bansuri, i.e., The Lowest pitch-Pa

But before going to that section we must know about the velocity of the sound. The velocity of the sound is generally considered as 331 m/s for rough calculation. The Velocity of the sound depends of the atmospheric temperature. The accurate formula for the Velocity of the sound is

                             C = 331.5 x Square Root [1 + ( T/273)]

                                                                             Where C = Velocity of the sound in m/s
                                                                                         T = Temperature in Celsius 



For example if the Temperature is 25 degree in winter, the Velocity of the Sound will be 343.42 m/s and when the temperature changes to 40 degree in  summer , the velocity of the sound will be 354.95 m/s

You can see from the above example that pitch changes due to the temperature variation, because the Velocity of the sound changes with the temperature, In the next entry we will see the correlation between the speed of the sound and Fundamental Pitch (Lowest Frequency)  and Fundamental length.         

Raag Bhimpalasi

In Raag Bhimpalasi, the komal ni in aroh is slightly higher then avroh

Raag Bilawal

Raag Bilawal was invented by Baiju Bawara, during the competition of music with Tansen. Baiju Bawara was belonging to gujarat. Tansen invented Raag Miyan ki malhar during this competition.

Khamaj

Rag khamaj is supposed to be originated from the folk tune played by the fisherman of the port "khambhat" situated in gujarat, india.

Finding k1 and k2

Now the question is aries that how to find k1 and k2. We know from the previous blog entry that k1 is equal to 0.3d. Now finding k2 theoretical is not possible (equation is there, but it is not giving accuracy). So k2 always founded practically.
When a designer starts to make bansuri he always keeps length more then the theoretical length .
After making blow hole, he starts to tune bansuri to lower Pa. He reduces the length of bansuri and consistently checks the pitch. When he get the correct pitch,he checks the actual length on which he arrived. Now we know theoretical length, actual length and k1, we can find k2. Which we will use for our further calculation and tone hole placement and diameter finding.

K1 and K2

K1 is the end correction due to diameter of bansuri while k2 is end correction due to blow hole
Hence total end correction will be
Theoritical length-k1-k2 = Actual length