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Ravi filled two cylinders with two gases (X and Y) of equal masses such that under similar conditions of temperature and pressure they occupy volumes of 2 l and 50 l , respectively . If he produces sound through both the gases inside the cylinders , then in which gas does sound travel with greater velocity ? Explain (Given that the value ofgamma is same for both the gases |
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Answer» Solution :Given , temperature and PRESSURE of two gases are similar when equal of gases are taken . Let the volume of 1st gas be `V_(X) = 2l` Let the volume of 2nd gas be `V_(Y) = 50 l` If sound waves are passed through both the gases , SPEEDS of sound waves depends only on the density of gases (SINCE temperature and pressure are similar ). `therefore S alpha (1)/(sqrtd) implies (S_(X))/(S_(Y)) = sqrt((d_(Y))/(d_(X))) ` `(S_(X))/(S_(Y)) = sqrt((m)/(V_(Y)) XX (V_(X))/(m)) ("since"d = (m)/(v))` `(S_(X))/(S_(Y)) = sqrt((2)/(50)) = 1 :5 , (S_(X))/(S_(Y)) = (1)/(5)` `S_(Y) = 5. S_(X)` Speed of a sound waves in gas 'y' is 5 TIMES that in gas 'x'. |
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