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At what temperatures (in 0^(@)C) will th...

At what temperatures (in `0^(@)C`) will the speed of sound in air be 3 times its value at `0^(@)C`?

Text Solution

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We have `v prop sqrtT implies (v _(2))/( v _(1)) = sqrt (( T _(2))/( T _(1)))`
` therefore (v _(1))/( 3 v _(1)) = sqrt (( 0 + 273)/( T _(2)))`
` therefore (1)/(9) = sqrt ((0 + 273)/(T _(2)))`
`therefore 1/9 = (273)/(T _(2))`
`therefore T _(2) = 2457 K = (2457 - 273)^(@)C`
`therefore T_(2) = 2184^(@)C`
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