Question

at what temperature the speed of sound in air will be 1.5 times its value at 27° C in air?

Answer 1

We know,
$v = \sqrt{T}$
Where, v= speed of sound, T=temperature.

Let, v1=speed of sound in air at t1 temperature.
v2=speed of sound in air at 27° C= speed of sound in air at 300 K.

Given, v1= 1.5 v2.

Putting in equation,
$v1 = \sqrt{t1} ....................(i)$
$v2 = \sqrt{300} .................(ii)$
Dividing equation (i) by (ii),
$\frac{v1}{v2} = \sqrt{ \frac{t1}{300} }$
$= > \frac{1.5v2}{v2} = \sqrt{ \frac{t1}{300} }$
$= > 1.5 = \sqrt{ \frac{t1}{300} }$
$= > {1.5}^{2} = \frac{t1}{300}$
$= > 2.25 \times 300 = t1$
= > t1 = 675 K or 402° C.