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Question
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?
Solution
Given:
Velocity of sound v1 = 340 m/s
Temperature T1 = 17°C = 17 + 273 = 290 K
Let the velocity of sound at a temperature T2 be 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.
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