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Sound Waves — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsSound Waves2 Marks
Question
The speed of sound as measured by a student in the laboratory on a winter day is 340m/s when the room temperature is $17^\circ C$. What speed will be measured by another student repeating the experiment on a day when the room temperature is $32^\circ C$?
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Answer

$\text{V}_1=330\text{m/s},\ \text{V}_2=?$$\text{T}_1=273+17=290\text{K},\ \text{T}_2=272+32=305\text{K}$
We know $\text{v}\propto\sqrt{\text{T}}$
$\frac{\sqrt{\text{V}_1}}{\sqrt{\text{V}_2}}=\frac{\sqrt{\text{T}_1}}{\sqrt{\text{T}}_2}$
$\Rightarrow\text{v}_2=\frac{\text{V}_1\times\sqrt{\text{T}_2}}{\sqrt{\text{T}_1}}$
$=340\times\sqrt{\frac{305}{290}}=349\text{m/s}$

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