   Chapter 14, Problem 43P

Chapter
Section
Textbook Problem

A stretched string fixed at each end has a mass of 40.0 g and a length of 8.00 m. The tension in the string is 49.0 N. (a) Determine the positions of the nodes and antinodes for the third harmonic. (b) What is the vibration frequency for this harmonic?

(a)

To determine
The position of the nodes and antinodes for the third harmonic.

Explanation

Given Info: The length of the string is 8.00m .

In the third harmonic, the standing wave contains three loops, each of length is,

λ2=L3

• λ is the wavelength of the standing wave,
• L is the length of the stretched string,

Rewrite the above relation in terms of wavelength.

λ=2L3

Substitute 8.00m for L to find λ .

λ=2(8.00m)3=5.33m

The position of nodes formed in the string for the third harmonic is,

N1=0

N2=λ2=5.33m2=2.67m

N3=λ=5.33m

N4=3λ2=3(5

(b)

To determine
The vibration frequency of the third harmonic.

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