Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11
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The Speed of Sound as Measured by a Student in the Laboratory on a Winter Day is 340 M S−1 When the Room Temperature is C17°. - Physics


The speed of sound as measured by a student in the laboratory on a winter day is 340 m s−1 when the room temperature is C17°. What speed will be measured by another student repeating the experiment on a day when the room temperature is 32°C?

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Velocity of sound v1 = 340 m/s
Temperature T1 = 17°C = 17 + 273 = 290 K
Let the velocity of sound at a temperature Tbe v2.
T2 = 32°C = 273 + 32 = 305 K
Relation between velocity and temperature:

\[v \propto \sqrt{T}\] 

\[So, \] 

\[\frac{v_1}{v_2} = \frac{\sqrt{T_1}}{\sqrt{T_2}}\] 

\[ \Rightarrow  v_2  = \frac{\sqrt{v_1} \times \sqrt{T_2}}{\sqrt{T_1}}\] 

\[\text { On  substituting  the  respective  values,   we  get: }\] 

\[ v_2  = 340 \times \sqrt{\frac{305}{290}} = 349  \text { m/s }\]

Hence, the final velocity of sound is 349 m/s.

Concept: Speed of Wave Motion
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HC Verma Class 11, 12 Concepts of Physics 1
Chapter 16 Sound Waves
Q 12 | Page 353
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