For open organ pipe frequency 1:2:3.

But you told 1:3:5.

How?

Fundamental frequency n=>425/5.

How did you write.

Why did you 425 decide by 5.

Explain sir.

Let's clarify the concepts surrounding the frequencies of an open organ pipe and how they relate to harmonics. The confusion seems to stem from the fundamental frequency and the harmonic series of an open pipe. In an open organ pipe, the frequencies of the harmonics are indeed related to the fundamental frequency, but the ratios can be a bit tricky to understand at first.

Understanding Open Organ Pipes

An open organ pipe allows air to vibrate freely at both ends, which means it can produce a series of harmonics. The fundamental frequency, or the first harmonic, is the lowest frequency produced by the pipe. The subsequent harmonics are integer multiples of this fundamental frequency.

Harmonic Series in Open Pipes

For an open pipe, the frequencies of the harmonics can be expressed as:

• 1st Harmonic (Fundamental): f₁ = n * (v / 2L)
• 2nd Harmonic: f₂ = 2f₁
• 3rd Harmonic: f₃ = 3f₁
• 4th Harmonic: f₄ = 4f₁
• 5th Harmonic: f₅ = 5f₁

Here, v is the speed of sound in air, L is the length of the pipe, and n is the harmonic number.

Frequency Ratios

When we talk about the frequency ratios of an open organ pipe, we refer to the fundamental frequency and its harmonics. The ratios are:

• 1st Harmonic: 1 (fundamental)
• 2nd Harmonic: 2 (first overtone)
• 3rd Harmonic: 3 (second overtone)

This means that the frequencies are in the ratio of 1:2:3, which corresponds to the fundamental and its first two overtones. However, when you mentioned 1:3:5, that ratio applies to the odd harmonics of a closed pipe, where only odd harmonics are present.

Calculating the Fundamental Frequency

Now, let's address the calculation of the fundamental frequency. You mentioned a frequency of 425 Hz and dividing it by 5. This seems to imply that you are looking for the fundamental frequency based on the fifth harmonic. The formula for the nth harmonic is:

fₙ = n * f₁

If we take the fifth harmonic (n=5) as 425 Hz, we can find the fundamental frequency:

f₁ = f₅ / 5 = 425 Hz / 5 = 85 Hz

So, the fundamental frequency in this case would be 85 Hz, and the harmonics would be:

• 1st Harmonic: 85 Hz
• 2nd Harmonic: 170 Hz
• 3rd Harmonic: 255 Hz
• 4th Harmonic: 340 Hz
• 5th Harmonic: 425 Hz

Conclusion

In summary, the frequencies of an open organ pipe are indeed in the ratio of 1:2:3 for the fundamental and its first two overtones. The confusion with 1:3:5 arises from the context of closed pipes, which only support odd harmonics. When calculating the fundamental frequency from a known harmonic, you divide by the harmonic number to find the base frequency. I hope this clears up the confusion!