An unstretched spring has a length of 0.30 m. When the spring is stretched to a total length of 0.60 m, it supports traveling waves moving at 4.5 m/s. How fast will waves travel on this spring if it is stretched to 0.90 m?
A)2.3 m/s
B)4.5 m/s
C)6.4 m/s
D)9.0 m/s
E)10.8 m/s

Question

Quizplus · Accepted Answer

Using the formula v=√(F/(μl)), where F is the tension in the spring, μ is the mass per unit length, and l is the unstretched length of the spring:

At a stretched length of 0.6 m: 
F = kΔx = k(0.3 m) = (40 N/m)(0.3 m) = 12 N
μ = m/l = F/(g*l) = (12 N)/(9.8 m/s^2 * 0.3 m) = 1.36 kg/m
v = √(F/(μl)) = √((12 N)/(1.36 kg/m * 0.6 m)) = 4.5 m/s

At a stretched length of 0.9 m:
F = kΔx = k(0.6 m) = (40 N/m)(0.6 m) = 24 N
μ = m/l = F/(g*l) = (24 N)/(9.8 m/s^2 * 0.3 m) = 2.72 kg/m
v = √(F/(μl)) = √((24 N)/(2.72 kg/m * 0.9 m)) = 6.4 m/s

Therefore, the waves will travel at 6.4 m/s when the spring is stretched to 0.90 m. The correct answer is (C).

An Unstretched Spring Has a Length of 0