Question

A pipe closed at one end and open at the other resonates at a fundamental frequency of 340 Hz. If the speed of sound in air is 340 m/s, the length of the pipe is:

• A. 0.25 m
• B. 0.50 m
• C. 1.00 m
• D. 2.00 m

Hint:

For a closed pipe, the fundamental frequency has a wavelength four times the length of the pipe: \( \lambda = 4L \). Use \( v = f \lambda \) to find \( L \).

Answer 1

The Correct Option is A

- For a pipe closed at one end and open at the other (closed pipe), the fundamental frequency corresponds to the first harmonic. The length \( L \) of the pipe is related to the wavelength \( \lambda \) by: \[ L = \frac{\lambda}{4} \]
- The speed of sound \( v \), frequency \( f \), and wavelength \( \lambda \) are related by: \[ v = f \lambda \implies \lambda = \frac{v}{f} \]
- Given \( v = 340 \, \text{m/s} \), \( f = 340 \, \text{Hz} \): \[ \lambda = \frac{340}{340} = 1 \, \text{m} \]
- Thus, the length of the pipe: \[ L = \frac{\lambda}{4} = \frac{1}{4} = 0.25 \, \text{m} \]
- This matches option (A).