COMEDK2023Evening ShiftPhysicsWaves and SoundActual
Two open organ pipes A and B of length 22 ~cm and 22.5 ~cm respectively produce 2 beats per sec when sounded together. The frequency of the shorter pipe is
Options
- A88 Hz
- B90 Hz
- C92 Hz
- D86 Hz
Correct answer
B. 90 Hz
Step-by-step solution
The fundamental frequency of an open organ pipe of length L is given by f = v 2L , where v is the speed of sound in air. Let v = 330 m/s be the standard speed of sound. For pipe A with length L_A = 22 cm = 0.22 m , the frequency is f_A = 330 2 0.22 = 330 0.44 = 750 Hz . For pipe B with length L_B = 22.5 cm = 0.225 m , the frequency is f_B = 330 2 0.225 = 330 0.45 = 733.33 Hz . The beat frequency is |f_A - f_B| = |750 - 733.33| = 16.67 Hz , which does not match the given 2 beats per second. This implies the speed of