AAMC FL Practice Exam

In the context of waves, what does the wavelength for standing waves fixed at both ends equal?

1. 4L/n

2. 2L/n

3. nL/2

4. L/n

The correct answer is: 2L/n

The wavelength for standing waves fixed at both ends is determined by the length of the medium where the waves are formed and the harmonic number. In a system like a string fixed at both ends, the length of the string (L) must accommodate a certain number of wavelengths, which is directly related to the harmonic number (n). For standing waves, the formula that relates wavelength (λ), length (L), and harmonic number (n) is given by: λ = 2L/n This equation represents the fact that for each harmonic (or mode of vibration) in a standing wave, the entire length of the string is effectively made up of an integer number of half-wavelengths. Specifically, the fundamental frequency (first harmonic) has one wavelength fitting into two time the length of the string, while higher harmonics have shorter wavelengths fitting into the same length. Thus, for standing waves fixed at both ends, the correct relationship shows that the wavelength is inversely proportional to the harmonic number, leading to the contention that as n increases, the wavelength decreases, supporting the properties of standing waves and harmonic systems.