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Question
The speed of sound in air at 0°C is 332 m/s. If it increases at the rate of 0.6 m/s per degree, what will be the temperature when the velocity has increased to 344 m/s?
Solution
Let the temperature at which the velocity of air becomes 344 m/s be T°C.
The increase in velocity of sound in air from 0°C to T°C = 344 - 332 = 12 m/s
Given,
The velocity of sound in air increases by 0.6 m/s for a 1°C rise in temperature.
Therefore, for a 1 m/s increase in the velocity of sound in air, the temperature should rise by `(1/0.6) ^circ`C.
For a 12 m/s increase in the velocity of sound in air, the temperature should rise by = `(12/0.6) ^circ"C"`
`= (12 xx 10)/(0.6 xx 10)`
`= 120/6`
`= 20^circ "C"`
Thus the speed of sound at 20°C will be 344 m/s.
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