Standing Waves Question

Question

A stretched spring is fixed at both ends. Students wiggle the string. They discover that at one frequency, they can create a standing wave with a wavelength of 𝜆_A = 0.7000 m. At a different frequency, they can form a standing wave with a wavelength of 𝜆_B = 0.6000 m. These are not necessarily the longest possible wavelengths. Based on these results, what is the probable length of the stretched spring?

Answer 1

You know that the standing waves require an integral number of half wavelengths: L = nλ_n/2 and L = mλ_m/2

The lowest integer solution of n(.6)/2 = m(.7)/2 is the most "likely" solution.

n(.6) = m(.7) The LCM is 4.2 (you can multiply through by 10 and it is clear that 42 is LCM), therefore, n = 7 and m = 6

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