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Elastic Waves. Acoustics.

Problem 4.171

A copper rod of length l=50 cml=50 \mathrm{~cm} is clamped at its midpoint. Find the number of natural longitudinal oscillations of the rod in the frequency range from 20 to 50kHz50 \mathrm{kHz}. What are those frequencies equal to?

Reveal Answer
 4.171. vn=2n+12lEρ=3.8(2n+1)kHz; four oscillations with  frequencies 26.6,34.2,41.8, and 49.4kHz\begin{aligned} &\text { 4.171. } v_{n}=\frac{2 n+1}{2 l} \sqrt{\frac{E}{\rho}}=3.8(2 n+1) \mathrm{kHz} ; \text { four oscillations with }\\ &\text { frequencies } 26.6,34.2,41.8, \text { and } 49.4 \mathrm{kHz} \end{aligned}
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