Assuming a speed of 2,000 m/s for the longitudinal vibrations, it would take approximately 0.009 seconds for the vibrations to travel from one child to the other along the 18-meter nylon cord.
The speed of a longitudinal wave in a string or cord can be calculated using the formula:
![\[ v = \sqrt{(T)/(\mu)} \]](https://img.qammunity.org/2024/formulas/physics/high-school/kke6ce3kzq9bgwejo3jo39j6c0nl66anv5.png)
Where:
- v = speed of the wave
- T = tension in the cord
-
= linear mass density of the cord
Firstly, let's find the linear mass density
of the nylon cord using the formula:
![\[ \mu = \rho \cdot A \]](https://img.qammunity.org/2024/formulas/physics/high-school/1nvtky9vh98sdw4w9qs9tnax4w2zj9ygon.png)
Where:
-

- A = cross-sectional area of the cord (not provided)
Unfortunately, without the cross-sectional area of the cord, we can't directly determine the linear mass density. However, if we assume a standard size for the cord, we can proceed with the calculation. For instance, if the cord is uniform and thin:
Let's assume a typical cross-sectional area for a nylon cord, say
(which might not accurately represent the cord's actual size).
Then:
![\[ \mu = \rho \cdot A \]](https://img.qammunity.org/2024/formulas/physics/high-school/1nvtky9vh98sdw4w9qs9tnax4w2zj9ygon.png)
![\[ \mu = 1.15 * 10^3 \, \text{kg/m}^3 * 1 * 10^(-6) \, \text{m}^2 \]](https://img.qammunity.org/2024/formulas/physics/high-school/rjdtg6go9d5sk5m4b6hxzb4vq72n1tmj0v.png)
![\[ \mu = 1.15 * 10^(-3) \, \text{kg/m} \]](https://img.qammunity.org/2024/formulas/physics/high-school/7xqy5xylbfn15xxmps4q57olwk1jybz7sb.png)
Next, to find the speed of the wave (v), we need the tension in the cord (T). Unfortunately, the tension is not given.
However, for longitudinal vibrations in a cord, the speed v generally ranges between 1,500 m/s to 3,000 m/s, depending on factors like tension and the cord's properties.
Using an approximate value within this range (let's use

The time taken for the vibrations to travel from one child to the other along the 18 m distance can be calculated using the formula:
![\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]](https://img.qammunity.org/2024/formulas/physics/high-school/v01q53l47g6bp4f8btph4wm58apkcj1con.png)
![\[ \text{Time} = \frac{18 \, \text{m}}{2,000 \, \text{m/s}} \]](https://img.qammunity.org/2024/formulas/physics/high-school/1aciqhtx5woop9a908uqkoyqk5xuccrc45.png)
![\[ \text{Time} = 0.009 \, \text{s} \]](https://img.qammunity.org/2024/formulas/physics/high-school/vowwr9p8lt1dareb7laqpm32z2ntk06m2h.png)