Laura and Elana are discussing how to solve the following problem: "A canary sits 10 m from the end of a 30-m-long clothesline, and a grackle sits 5 m from the other end. The rope is pulled by two poles that each exert a 200-N force on it. The mass per unit length is 0.10 kg/m. At what frequency must you vibrate the line in order to dislodge the grackle while allowing the canary to sit undisturbed

Answer: 2.24Hz

Explanation:

We have to calculate the speed of the wave on the rope and also determine the frequency that will produce a standing wave with a node located at 10m from the end.

Data;

Length of the clothesline L = 30m

The canary sits 10m from the end

The grackle sits 5m from the other end

Force (F) on the two poles = 200N

Mass per unit length (m) = 0.10kg/m

Speed of the wave on the string?

V = [F/m]½

V = [200/0.10]½

V = 44.72m/s

V = 45m/s

For a minimum frequency of vibration, the distance between the two ends of the canary must be equal to y/2

Note y represents the greek alphabet lambda

y/2 = 10m

y = 10*2

y = 20m

Frequency (f) of the vibration of the string = v/y

f = v / y

f = 44.72 / 20

f = 2.24 Hz