THe velocity of sound in air at 16oC is 340ms-1. What will it be when the pressure is doubled and its temperature raised to 127ºC?
The velocity of sound in air, V∝√T, where T is absolute temperature
Thus V = K√T or K = V/T
V is independent of pressure and density at a fixed temperature.
∴ V1/√T1 = V2/√T2
T1 = 16 + 273 = 289K, V1 = 340ms-1
T2 = 127 + 273 = 400K, V2 = ?
| 340 | = | V2 |
| √289 | √400 |
| ∴ V2 = | 340√400 |
| _√289 |
= 400m/s
There is an explanation video available below.
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