Question

Speed of sound in air is found to be 344$\frac{m}{s}$ at 80${}^{\circ }$ C. Find the change in speed of sound for a 1${}^{\circ }$ C increase in temperature.

• A. 1 m/s
• B. 0.6 m/s
• C. 0.01 m/s
• D. None of these

Answer 1

The correct option is D

None of these

Given at 20${}^{\circ }$C v = 344 m/s

T${}_1$ = 273 + 20 = 293 k

T${}_2$ = T1 + ∆T

v${}_1$= 344

Let $v_2=v_1+\Delta V$

We know

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

$\frac{v_2+\Delta v}{v_1}=\sqrt{\frac{T_1+\Delta T}{T_1}}$

$1+\frac{\Delta v}{v_1}=\sqrt{1+\frac{\Delta T}{T_1}}$

$1+\frac{\Delta v}{v_1}=1+\frac{1}{2}\frac{\Delta T}{T_1}$ (Using approximate)

$\Rightarrow \Delta v=\frac{1}{2}\frac{\Delta T}{T_1}{v}_1=\frac{1}{2}\frac{1}{293}344$

= 0.587 $\Delta$v = 0.6 $\frac{m}{s}$.