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Chapter 17: Q. 21 (page 483)

A longitudinal standing wave can be created in a long, thin aluminum rod by stroking the rod with very dry fingers. This is often done as a physics demonstration, creating a high-pitched, very annoying whine. From a wave perspective, the standing wave is equivalent to a sound standing wave in an open-open tube. As FIGURE EX17.21 shows, both ends of the rod are antinodes. What is the fundamental frequency of a 2.0-m-long aluminum rod?

Short Answer

Expert verified

The fundamental frequency of a 2.0-m-long aluminum rod is,1605Hz.

Step by step solution

01

Given data

Length of the aluminum rod is, L=2m

Both ends of the rod are antinodes. So, the rod is vibrating in the fundamental mode.

Consider speed of sound in aluminum is,v=6420m/s

02

Determination of frequency

For fundamental mode, the wavelength of sound wave can ne written as, λ1=2L

Therefore, the frequency of the longitudinal standing wave is,

f=vλ1⇒f=6420m/s2L⇒f=6420m/s2×2m⇒f=1605Hz

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