question_answer 50)

                  At what temperature (in \[^{o}C\]) will the speed of sound in air be 3 times its value of \[{{O}^{o}}C\]?

Answer:

                  \[\upsilon \propto \,\sqrt{T}\].                 Let \[{{\theta }^{o}}C\] be the temperature at which                 \[\upsilon =\,3\] times \[\upsilon \] at \[{{0}^{o}}c\].                 \[\therefore \] \[\frac{{{\upsilon }_{\theta }}}{{{\upsilon }_{\theta }}}\,=\sqrt{\frac{273+\theta }{273}}\]                 or \[3=\,\sqrt{\frac{273+\theta }{273}}\,\] or \[273\,+\,\theta \,=\,9\,\times \,273\]                 \[\therefore \] \[\theta =\,283\,\times \,8\,={{2184}^{o}}C\]