How does the speed of sound increasing when the temperature increases be explained using a parallel to the speed of a wave on a string? Since the wave on a string is transverse and only depends on tension and mass density of the medium, how would this be relevant to the speed of sound (which is longitudinal?)

Question
Asked Oct 20, 2019

How does the speed of sound increasing when the temperature increases be explained using a parallel to the speed of a wave on a string? Since the wave on a string is transverse and only depends on tension and mass density of the medium, how would this be relevant to the speed of sound (which is longitudinal?)

check_circleExpert Solution
Step 1

Speed of transverse wave in a string is given by the equation:

Where T is tension in the string
-is the linear mass density of the string
From the above equation we can say that as the linear mass density decreases the speed of the
wave in the string increases.
help_outline

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Where T is tension in the string -is the linear mass density of the string From the above equation we can say that as the linear mass density decreases the speed of the wave in the string increases.

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Step 2

The speed of sound in a ...

=
Where E is the bulk modulus of the gas,
And p Is the density of the gas.
Similarly, we can say that as the density of the gas decreases the speed of the sound in the gas
increases
help_outline

Image Transcriptionclose

= Where E is the bulk modulus of the gas, And p Is the density of the gas. Similarly, we can say that as the density of the gas decreases the speed of the sound in the gas increases

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