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Expert-verified Found in: Page 483 ### Physics for Scientists and Engineers: A Strategic Approach with Modern Physics

Book edition 4th
Author(s) Randall D. Knight
Pages 1240 pages
ISBN 9780133942651 # A bass clarinet can be modeled as a 120-cm-long open-closed tube. A bass clarinet player starts playing in a 20°C room, but soon the air inside the clarinet warms to where the speed of sound is 352 m/s. Does the fundamental frequency increase or decrease? By how much?

The warmer air temperature increases the fundamental frequency by $1.9Hz$.

See the step by step solution

## Given information

The length of the open-closed tube is $L=120cm=1.20m$

The speed of sound is $v=352m/s$.

## The fundamental frequency at v=343 m/s

Assume that the strings of the violin have the same tension and same length and therefore the same fundamental wavelength.

The fundamental frequency at the cool room temperature where the speed of sound is $343m/s$.

role="math" localid="1650031107837" ${f}_{cool}=\frac{v}{4L}\phantom{\rule{0ex}{0ex}}=\frac{343}{4×1.2}\phantom{\rule{0ex}{0ex}}=71.46Hz$

## Increase in the fundamental frequency

Take the ratio ${f}_{hot}$ and ${f}_{cool}$.

Thus, the warmer air temperature increases the fundamental frequency.

role="math" localid="1650031592581" ${f}_{hot}-{f}_{cool}=73.33-71.46\phantom{\rule{0ex}{0ex}}\approx 1.9Hz$

Therefore, the warmer air temperature increases the fundamental frequency by $1.9Hz$. ### Want to see more solutions like these? 