At What Temperature the Velocity of Sound Is Double Than at the Temperature 27°C – Full Guide
In physics, the question of at what temperature the velocity of sound is double than at the temperature 27°C is solved using the relationship between air temperature and sound speed. This guide explains the answer clearly.
Relation Between Temperature and Velocity of Sound
The velocity of sound in air increases with temperature. In general, sound travels faster in warmer air because the molecules move more quickly. The approximate formula that relates sound speed to temperature is:
v = 331 + 0.6 × T (where v is sound velocity in m/s and T is temperature in °C).
Calculating Double the Velocity at 27°C
At 27°C, the speed of sound is approximately:
v = 331 + 0.6 × 27 ≈ 347.2 m/s
To find when it becomes double, we set:
2 × 347.2 ≈ 694.4 m/s
Substitute into the sound formula and solve for temperature:
- 694.4 = 331 + 0.6T
- 0.6T = 694.4 − 331 = 363.4
- T ≈ 605.7°C
The actual temperature required is very high and not commonly found in normal atmospheric conditions.
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At What Temperature the Velocity of Sound Is Double Than at the Temperature 27°C