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? "

Explanation:

Given:

Length of a rope,

Position of Canary on the rope from one end,

Position of Grackle on the rope from another end,

Tension in the rope,

linear mass distribution on the rope,

We have for the speed of wave on the string:

For canary to be undisturbed we need a node at this location.

Also, at the end close to Canary there must be a node to avoid any change in pattern of vibration.

So,

the distance between Canary and the closer end must be equal to half the wavelength.

∴Wavelength of wave to be produced = 20 m. This will give us nodes at the multiples of 10 and anti-nodes at the multiples of 5.

Now, frequency: