For a spring that obeys Hooke's law, the tension in the spring is proportional to the stretched length of the spring τ=k(L−L_o), where L and L_o are the length of the stretched and unstretched spring, respectively, and k is the spring constant. The mass density of the spring is μ=M/L and the wave velocity is v=sqrt(τ/μ). Substitution of these expressions into Eq. 6.1 shows that the frequency of the standing waves depends on the length of the spring L as f=n/2*sqrt(k/M)*sqrt(1−L_o/L). The fundamental frequency of the standing wave is measured for two different stretched lengths, L/A/L_o=5 and L_B/L_o=2. What is the expected ratio of the frequencies, fA/fB ?

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Stretched string

A stretched string is a wire which is made up of any metal that must have a larger length compared to its thickness. The ends of the wire are fixed, and when they oscillate or are plucked, it produces two reflected transverse waves of the same frequency and same amplitude. The waves or pulses are traveling in alternate directions and superimpose with one another. This waveform is named standing or stationary waves.