Question

# What is the algebraic relationship between the resonant wavelength, λ, and length of an open-closed tube, L, for the n=1,3,5, and 7 harmonics. The options below refer to the following expressions 1. λ= 2L/52. λ= 2L/73. λ=5L4. λ=3L5. λ = 4L/36. λ=4L7.λ = L8. λ= 4L/79. λ=7L10. λ= 4L/5

Answer

{λ1: 4L, λ3: 4L/3, λ5: 4L/5, λ7: 4L/7}

- Q: What is the general formula for the resonant wavelength of an open-closed tube for the n-th harmonic? A: The general formula is λn = 4L/n, where L is the length of the tube and n is the harmonic number.
- Q: Using the general formula derived in step 1, what are the values of λ for the n=1,3,5, and 7 harmonics? A: For n=1, λ=4L/1=4L; for n=3, λ=4L/3; for n=5, λ=4L/5; for n=7, λ=4L/7.