Question

Length of an organ pipe open at both ends is 34 cm. If velocity of sound is 340 m/s, then the frequency of 2nd overtone is:

• A. 2400 Hz
• B. 1000 Hz
• C. 1500 Hz
• D. 2000 Hz

Hint:

In an organ pipe open at both ends, the harmonics are integer multiples of the fundamental frequency, with the second overtone being the third harmonic.

Answer 1

The Correct Option is C

Step 1: Frequency of Harmonics in an Organ Pipe.
The frequency of the \( n \)-th harmonic in an open organ pipe is given by: \[ f_n = \frac{n v}{2L} \] where \( v \) is the velocity of sound and \( L \) is the length of the pipe. The second overtone corresponds to the third harmonic. Substituting the values: \[ f_3 = \frac{3 \times 340}{2 \times 0.34} = 1500 \, \text{Hz} \] Step 2: Final Answer.
Thus, the frequency of the second overtone is 1500 Hz.