# The speed of sound in air is 332m/s at 0 C. At what temperature the speed become one halg of that of 0 C

speed of sound is directly proportional to square root of temperature.

so,

$\frac{{v}_{1}}{{v}_{2}}=\sqrt{\frac{{T}_{1}}{{T}_{2}}}\phantom{\rule{0ex}{0ex}}{v}_{1}=332m/s\phantom{\rule{0ex}{0ex}}{T}_{1}=273K\phantom{\rule{0ex}{0ex}}{v}_{2}=\frac{{v}_{1}}{2}\phantom{\rule{0ex}{0ex}}{T}_{2}=?\phantom{\rule{0ex}{0ex}}\frac{1}{2}=\sqrt{\frac{273}{{T}_{2}}}\phantom{\rule{0ex}{0ex}}squaringonbothside,\phantom{\rule{0ex}{0ex}}{T}_{2}=273\times 4=1092K\phantom{\rule{0ex}{0ex}}Regards$

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