Which expression gives the fundamental frequency f1 in terms of the wave speed v and length L?

Which expression gives the fundamental frequency f1 in terms of the wave speed v and length L?

• A. f1 = v/L
• B. f1 = 2L/v
• C. f1 = v/(2L)
• D. f1 = 2v/L

Answer: (C)

The fundamental frequency comes from the fact that only certain wavelengths fit into the length with fixed ends. For the fundamental, half a wavelength fits into the length, so L = λ1/2, giving λ1 = 2L. Since frequency is speed divided by wavelength, f1 = v/λ1 = v/(2L). Other expressions don’t match this fundamental condition: v/L would correspond to a higher harmonic, and 2L/v is the period T, not the frequency. The form 2v/L would be twice the fundamental frequency, matching a different harmonic.

The fundamental frequency comes from the fact that only certain wavelengths fit into the length with fixed ends. For the fundamental, half a wavelength fits into the length, so L = λ1/2, giving λ1 = 2L. Since frequency is speed divided by wavelength, f1 = v/λ1 = v/(2L).

Other expressions don’t match this fundamental condition: v/L would correspond to a higher harmonic, and 2L/v is the period T, not the frequency. The form 2v/L would be twice the fundamental frequency, matching a different harmonic.