Question

Velocity of sound in an open organ pipe is 330 m/s. The frequency of the wave is 1.1 kHz and the length of the tube is 30 cm. To which harmonic does this frequency correspond?

• A. 5th
• B. 4th
• C. 3rd
• D. 2nd

Hint:

In an open organ pipe, the harmonics are integer multiples of the fundamental frequency. The second harmonic corresponds to a wavelength that is equal to the length of the pipe.

Answer 1

The Correct Option is D

The velocity of sound \( v \) in an open organ pipe is given by the formula: \[ v = f \cdot \lambda \] where \( f \) is the frequency, and \( \lambda \) is the wavelength of the wave. The fundamental frequency of an open organ pipe is given by: \[ \lambda_1 = 2L \] where \( L \) is the length of the tube. For the second harmonic, the wavelength \( \lambda_2 \) is: \[ \lambda_2 = L \] Using the relationship \( v = f \cdot \lambda \), we find that the second harmonic corresponds to the frequency of 1.1 kHz. 
Therefore, the correct harmonic is the second harmonic. Hence, the correct answer is (d).