   Chapter 14, Problem 80AP

Chapter
Section
Textbook Problem

A student stands several meters in front of a smooth reflecting wall, holding a board on which a wire is fixed at each end. The wire, vibrating in its third harmonic, is 75.0 cm long, has a mass of 2.25 g, and is under a tension of 400. N. A second student, moving toward the wall, hears 8.30 beats per second. What is the speed of the students approaching the wall?

(a)

To determine
The speed of the student approaching the wall.

Explanation

Given Info: The length of the wire is 75.0 cm, mass of the wire 2.25 g, and tension in the wire is 400 N

Formula to calculate the fundamental frequency of the vibrating wire is,

f=n2LTμ (1)

• f is the fundamental frequency.
• n is the harmonic number.
• T is the tension.
• μ is the mass per unit length.

Rewrite the equation (1) in terms of mass per unit length.

f=n2LTm/L

Substitute 3 for n, 75.0 cm for L, 400 N for T, and 2.25 g for m we get f.

f=32(75.0cm)(0.01m1cm)(400N)(2.2g)(0.001kg1g)/(75.0cm)(0.01m1cm)=730.3Hz

Thus, the fundamental frequency of the wire vibrating in its third harmonic number is 730.3 Hz.

Formula to calculate the primary source of the frequency is,

fP=f(vv0v) (2)

• fP is the primary source of the frequency to the observer.
• f is the fundamental frequency of the wire.
• v is the speed of the sound in air.
• v0 is the speed of the student

(b)

To determine
The number of Moons can fit inside the Earth.

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