Question

(II) Two children are sending signals along a cord of total mass 0.50 kg tied between tin cans with a tension of 35 $\mathrm{N}$ . It takes the vibrations in the string 0.50 $\mathrm{s}$ to go from one child to the other. How far apart are the children?

Name: Problem 13, Chapter 15: Physics for Scientists and Engineers with Modern Physics
Uploaded: 2020-11-10T16:50:44-08:00
Duration: 1 min 48 s
Channel: Sachin Rao
Description: (II) Two children are sending signals along a cord of total mass 0.50 kg tied between tin cans with a tension of 35 N . It takes the vibrations in the string 0.50 s to go from one child to the other. How far apart are the children?

   (II) Two children are sending signals along a cord of total mass 0.50 kg tied between tin cans with a tension of 35 $\mathrm{N}$ . It takes the vibrations in the string 0.50 $\mathrm{s}$ to go from one child
to the other. How far apart are the children?

Physics for Scientists and Engineers with Modern Physics

Douglas C. Giancoli 4th Edition

Chapter 15, Problem 13

Instant Answer

Solved by Expert Sachin Rao

11/10/2020

Step 1

Step 1: We know that the speed of a wave is given by the formula $v = \sqrt{\frac{T}{\mu}}$, where $T$ is the tension in the string and $\mu$ is the linear mass density of the string. Show more…

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(II) Two children are sending signals along a cord of total mass 0.50 kg tied between tin cans with a tension of 35 $\mathrm{N}$ . It takes the vibrations in the string 0.50 $\mathrm{s}$ to go from one child to the other. How far apart are the children?

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Key Concepts

Time-Distance Relationship in Wave Motion

This concept involves using the wave speed along with the time taken for a wave to travel a given distance. It connects the physical parameters of the medium (tension and mass density) to practical measurements, allowing the calculation of distances when wave travel time is known.

Wave Propagation on a String

This concept deals with how mechanical waves travel along a stretched string. The speed at which waves propagate depends primarily on the tension in the string and its mass per unit length. Understanding this relationship is crucial for analyzing wave behavior in various physical contexts.

Tension and Linear Mass Density

Tension is the force stretching the string, while linear mass density is the mass of the string per unit length. Their relationship is given by the formula for wave speed on a string, v = ?(T/?), which demonstrates how increasing tension or decreasing mass density results in faster wave travel.

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