Final answer:
The length of an organ pipe, which is closed at one end and has a fundamental frequency of 275 Hz, is found using the quarter wavelength principle. Assuming a speed of sound of 343 m/s, the length of the pipe is calculated to be approximately 31.2 cm.
Step-by-step explanation:
Finding the Length of an Organ Pipe Closed at One End
To find the length of an organ pipe that is closed at one end and has a fundamental frequency of 275 Hz, we need to understand how standing waves function in such pipes. In a pipe closed at one end, the standing wave has a node at the closed end and an antinode at the open end. The length of the pipe corresponds to a quarter wavelength (¼λ) of the fundamental frequency.
The speed of sound in air varies with temperature, but at room temperature (approximately 20°C), it is typically around 343 m/s. Using the formula for the fundamental frequency f = v/4L, where f is the frequency, v is the speed of sound and L is the length of the pipe, we can rearrange the formula to solve for L:
L = v/4f
For a fundamental frequency of 275 Hz and assuming the speed of sound is 343 m/s, the length of the pipe can be calculated as:
L = 343 m/s / (4 × 275 Hz) = 0.312 m or 31.2 cm.
Therefore, the length of the organ pipe closed at one end with a fundamental frequency of 275 Hz is approximately 31.2 cm.