Question

A section of drainage culvert 1.23 m in length makes a howling noise, when the wind blows across its open ends. Speed of sound in air is 343ms⁻¹. The frequency of the first harmonic of the culvert, if it is cylindrical in shape and open at both ends, is:

A 239 Hz
B 189 Hz
C 200 Hz
D 139 Hz

Answer 1

The frequency of the first harmonic or fundamental frequency for an open pipe that is 1.23 m long, when the speed of sound is 343 m/s, is calculated as 139 Hz, making the correct answer 139 Hz.

Step-by-step explanation:

The frequency of the first harmonic or fundamental frequency for a cylindrical tube open at both ends that is 1.23 m in length can be calculated using the formula for the fundamental frequency of an open pipe, which is f = v / (2L), where f is the frequency, v is the speed of sound, and L is the length of the tube.

Given that the speed of sound, v, is 343 m/s, and the length of the tube, L, is 1.23 m, we can substitute these values into the formula:

f = 343 m/s / (2 * 1.23 m) = 343 m/s / 2.46 m ≈ 139.43 Hz, which we round to 139 Hz.

Therefore, the correct answer is D 139 Hz.