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Summary

This video tutorial explains how to calculate the wavelength of the second harmonic of an open-ended pipe, using the example of a flute. The script walks viewers through key concepts like harmonics, speed of sound, and the relationship between pipe length and frequency. By applying the formula for harmonic frequencies in open pipes, the tutorial demonstrates how to determine the length of the pipe and then calculate the wavelength for the second harmonic. Ultimately, the answer for the wavelength of the second harmonic is determined to be 20 cm, helping viewers better understand the principles of sound waves and harmonics in pipes.

Takeaways

• 😀 A flute (seruling) is an open-ended pipe with both ends open, which affects its harmonic properties.
• 😀 The frequency of the second harmonic (F2) for this flute is given as 1700 Hz.
• 😀 The speed of sound in air is 340 m/s, which is crucial for calculating the length of the pipe.
• 😀 The formula to calculate the frequency of the nth harmonic in an open-ended pipe is: F_n = (n+1) * v / (2L).
• 😀 The harmonic number (n) for the fundamental is 0, for the first overtone it’s 1, and for the second overtone, it’s 2.
• 😀 For the second harmonic, n = 2, and using the formula, we calculate the length of the flute to be 0.3 meters.
• 😀 The wavelength for the second harmonic can be calculated using the formula: λ_n = 2 * L / (n+1).
• 😀 Using the length of the flute (L = 0.3 m) and n = 2, the wavelength for the second harmonic (λ_2) is 0.2 meters.
• 😀 The result for the wavelength (λ_2 = 0.2 m) is equivalent to 20 cm, as 1 meter equals 100 cm.
• 😀 The correct answer for the wavelength of the second harmonic is 20 cm, corresponding to option C.

Q & A

What type of pipe is discussed in the video?

The video discusses an open organ pipe, specifically a flute (seruling) with both ends open.

What is the frequency of the second harmonic (F2) for the flute?

The frequency of the second harmonic (F2) is 1700 Hz.

What is the speed of sound in the air, as mentioned in the video?

The speed of sound in air is given as 340 m/s.

What is the formula for calculating the frequency of harmonics in an open pipe?

The formula for the frequency of harmonics in an open pipe is F_n = (n + 1) * v / 2l, where F_n is the frequency, n is the harmonic number, v is the speed of sound, and l is the length of the pipe.

How do you determine the harmonic number for the second harmonic?

The harmonic number for the second harmonic is 2, as it is the second overtone in the series.

What is the length of the flute (pipe) calculated in the video?

The length of the flute (pipe) is calculated to be 0.3 meters (30 cm).

How is the wavelength of the second harmonic (λ2) calculated?

The wavelength of the second harmonic (λ2) is calculated using the formula λ = 2 * l / (n + 1), where l is the length of the pipe and n is the harmonic number.

What is the wavelength of the second harmonic for this flute?

The wavelength of the second harmonic (λ2) is 0.2 meters, which is equivalent to 20 cm.

How is the conversion from meters to centimeters done in the solution?

To convert meters to centimeters, the value in meters is multiplied by 100. For example, 0.2 meters becomes 20 cm.

What is the correct answer for the wavelength of the second harmonic in this problem?

The correct answer for the wavelength of the second harmonic is 20 cm, which corresponds to option C in the choices.