   Chapter 13, Problem 57P

Chapter
Section
Textbook Problem

Tension is maintained in a string as in Figure P13.57. The observed wave speed is v = 24.0 m/s when the suspended mass is m = 3.00 kg. (a) What is the mass per unit length of the string? (b) What is the wave speed when the suspended mass is m = 2.00 kg? Figure P13.57

(a)

To determine
The mass per unit length of the string.

Explanation

Given info: The speed of the wave on the string is 24.0ms-1 . The mass of the suspended object is 3.00kg .

The tension on the string will be the weight of the object hung from the string.

F=mg (1)

• m is the mass of the object
• g is the free fall acceleration

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 string or the linear density of the string

Solving for μ ,

μ=Fv2 (2)

From (1) and (2),

μ=mgv2

Substitute 3.00 kg for m, 24.0ms-1 for v , and 9

(b)

To determine
The speed of the wave when mass m=2.00kg is suspended.

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