AAMC FL Practice Exam

Which equation represents the relationship in a closed pipe with one end open?

1. n1sinθ1 = n2sinθ2

2. 1/o + 1/i = 1/f

3. Wavelength = 4L/n

4. Power = 1/f

The correct answer is: Wavelength = 4L/n

In a closed pipe with one end open, the condition for standing waves leads to specific patterns for the wavelengths of the sound produced within the pipe. The correct equation, which describes this relationship, indicates that the wavelength is equal to four times the length of the pipe divided by an integer n, where n represents the harmonic number (specifically, the odd integers: 1, 3, 5, etc.). In this scenario, the closed end of the pipe is a node (point of no displacement), while the open end is an antinode (point of maximum displacement). This setup necessitates that only odd harmonics can form in the pipe, thus giving rise to the relationship that the wavelengths are constrained by a factor of 4 to the length of the pipe. The equation encompasses the concept that the fundamental frequency (first harmonic) occurs when n = 1, and it can be expanded for additional harmonics by considering only odd values of n. Thus, this equation captures the essence of wave behavior in closed-end pipes, which is critical for understanding acoustics and wave mechanics in physics.