Question

Two strings are respectively 1.00 m and 2.00 m long. Which of the following wavelengths, in meters, could represent harmonics present on both strings?

1) 0.800, 0.670, 0.500
2) 1.33, 1.00, 0.500
3) 2.00, 1.00, 0.500
4) 2.00, 1.33, 1.00
5) 4.00, 2.00, 1.0

Answer 1

5) 4.00, 2.00, 1.0

Step-by-step explanation:

wave equation is given as;

F₀ = V / λ

Where;

F₀ is the fundamental frequency = first harmonic

Length of the string for first harmonic is given as;

L₀ = (¹/₂) λ

λ = 2 L₀

when L₀ = 1

λ = 2 x 1 = 2m

when L₀ = 2m

λ = 2 x 2 = 4m

For First harmonic, the wavelength is 2m, 4m

For second harmonic;

L₁ = (²/₂)λ

L₁ = λ

When L₁ = 1

λ = 1 m

when L₁ = 2

λ = 2 m

For second harmonic, the wavelength is 1m, 2m

Thus, the wavelength that could represent harmonics present on both strings is 4m, 2m, 1 m