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 ?

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 ?