Question

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

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

Step-by-step solution

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,$v=6420m/s$

Determination of frequency

For fundamental mode, the wavelength of sound wave can ne written as, ${\lambda }_1=2L$

Therefore, the frequency of the longitudinal standing wave is,

$$\begin{gathered} f=\frac{v}{{\lambda }_1} \\ \Rightarrow f=\frac{6420m/s}{2L} \\ \Rightarrow f=\frac{6420m/s}{\left(2\times 2\right)m} \\ \Rightarrow f=1605Hz \end{gathered}$$