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Q. 19

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
Found in: Page 483

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Short Answer

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 1.9 Hz.

See the step by step solution

Step by Step Solution

Given information

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

The speed of sound is v=352 m/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 343 m/s.

role="math" localid="1650031107837" fcool=v4L=3434×1.2=71.46 Hz

Increase in the fundamental frequency

Take the ratio fhot and fcool.

fhotfcool=vhot4Lvcool4L=352343fhot=352343×71.46=73.3 Hz

Thus, the warmer air temperature increases the fundamental frequency.

role="math" localid="1650031592581" fhot-fcool=73.33-71.461.9 Hz

Therefore, the warmer air temperature increases the fundamental frequency by 1.9 Hz.

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