# At What Temperature Will the Speed of Sound Be Double of Its Value at 0°C? - Physics

Sum

At what temperature will the speed of sound be double of its value at 0°C?

#### Solution

Let the speed of sound T1 be v1,
where T1 = 0˚ C = 273 K.
Let T2 be the temperature at which the speed of sound (v2) will be double its value at 0˚ C.
As per the question,
v2 = 2v1.

$v \propto \sqrt{T}$

∴​

$\frac{{v_2}^2}{{v_1}^2} = \frac{T_2}{T_1}$

$\Rightarrow \frac{\left( 2 v_1 \right)^2}{{v_1}^2} = \frac{T_2}{273}$

$\Rightarrow T_2 = 273 \times 4 = 1092 K$

To convert Kelvin into degree celsius:

$T_2 = \left( 273 \times 4 \right) - 273 = 819^\circ C$

Hence, the temperature (T2 ) will be 819˚ C

Concept: Wave Motion
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#### APPEARS IN

HC Verma Class 11, 12 Concepts of Physics 1
Chapter 16 Sound Waves
Q 13 | Page 353