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Chapter 17: Q. 15 (page 483)

FIGURE EX17.15 shows a standing sound wave in an 80-cm-long tube. The tube is filled with an unknown gas. What is the speed of sound in this gas?

Short Answer

Expert verified

The speed of sound in the gas is400m/s.

Step by step solution

01

Given information

A standing sound wave in an 80-cm-long tube is shown below

02

Speed of sound in gas

At the ends of the tube, the gas molecules exhibit maximum displacement, resulting in antinodes at the ends.

There is another antinode in the middle of the tube.

Thus, this is the m=2mode and the wavelength of the standing wave is equal to the length of the tube, that is, λ=0.80m

The relation between wavelength, frequency, and speed of the wave is given by v=fλ.

Substitute the given values

v=500×0.80=400m/s

Therefore, the speed of sound in the gas is400m/s.

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