   Chapter 14, Problem 46P

Chapter
Section
Textbook Problem

A distance of 5.00 cm is measured between two adjacent nodes of a standing wave on a 20.0-cm-long string. (a) In which harmonic number n is the string vibrating? (b) Find the frequency of this harmonic if the string has a mass of 1.75 × 10−2 kg and a tension of 875 N.

(a)

To determine
The harmonic number in the vibrating string.

Explanation

Given Info: The distance between the two adjacent nodes is 5.00 cm and length of the standing wave formed in the string is 20.0 cm

Formula to calculate the harmonic number is,

λn=λ1n (1)

• λn is the distance of the odd number of harmonic wavelength.
• λ1 is the fundamental wavelength.
• n is the harmonic number.

Conclusion:

Rewrite the equation (1) in terms of n.

n=λ1λn

Substitute 20

(b)

To determine
The frequency for the harmonic number n=4 in the vibrating string.

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