   Chapter 13, Problem 56P

Chapter
Section
Textbook Problem

A string is 50.0 cm long and has a mass of 3.00 g. A wave travels at 5.00 m/s along this string. A second string has the same length, but half the mass of the first. If the two strings are under the same tension, what is the speed of a wave along the second string?

To determine
The speed of a wave on the second string.

Explanation

Given info: The length of the first string is 50.0cm . The mass of the string is 3.00g . The speed of the wave is 5.00ms-1 . The second string has the same length, but half the mass of the first. The two strings are under the same tension.

The linear density of the string will be,

μ=mL

• m is the total mass of the string
• L is the length of the string

The linear density of the first string is,

μ1=m1L

• m1 is the mass of the first string

The linear density of the second string is,

μ2=m2L

• m2 is the mass of the first string.

Since m2=m12 .

Substitute m1/2 for m2 in μ2 .

μ2=m12L=μ12

The wave speed in a stretched string is given as,

v=Fμ

• v is the wave speed
• F is the tension in the string
• μ is the mass per unit length of the stri

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