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 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?

• A. 333$\frac{m}{s}$
• B. 340$\frac{m}{s}$
• C. 350$\frac{m}{s}$
• D. None of these

Answer 1

The correct option is C

350$\frac{m}{s}$

Given at T = 17${}^{\circ }$ C or 290 k

Speed was 340 $\frac{m}{s}$

To find speed at T = 32${}^{\circ }$ or 305 k

So velocity of sound and Temperature

Gives the relation

$v=\sqrt{\frac{\gamma RT}{M}}$

$v\alpha \sqrt{T}$

$\Rightarrow \frac{v_1}{v_2}=\sqrt{\frac{T_1}{T_2}}$

$\Rightarrow \frac{340}{v_2}=\sqrt{\frac{290}{305}}$

$v_2=350\frac{m}{s}$