Question

Ratio of wavelength of first two modes of open pipe

• A. 2:1
• B. 1:2
• C. 1:1
• D. 1:4

Hint:

In an open pipe, the wavelength of the fundamental is twice the length of the pipe, and the wavelength of the first overtone is equal to the length of the pipe. Hence, the ratio of the wavelengths is 2:1.

Answer 1

The Correct Option is A

In an open pipe, both ends are open, and the modes of vibration of the pipe are such that there is a displacement antinode at both ends. The wavelengths for the fundamental and the first overtone (second harmonic) in an open pipe are as follows: - For the first mode (fundamental frequency), the wavelength \( \lambda_1 \) is given by: \[ \lambda_1 = 2L \] where \( L \) is the length of the pipe. - For the second mode (first overtone), the wavelength \( \lambda_2 \) is given by: \[ \lambda_2 = L \] Thus, the ratio of the wavelengths of the first two modes is: \[ \frac{\lambda_1}{\lambda_2} = \frac{2L}{L} = 2:1 \] So, the correct answer is 2:1.