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?
-
A.
400 ms-1 -
B.
4,000 ms-1 -
C.
8,000 ms-1 -
D.
160,000 ms-1
Correct Answer: Option A
Explanation
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