The velocity of sound in air (v) pressure (p) and density of air (d) are related as v α pxdy the value of 'x' and 'y' respectively are

Question

The velocity of sound in air (v) pressure (p) and density of air (d) are related as v α pxdy the value of 'x' and 'y' respectively are

Infinity Learn · Accepted Answer

v α px $$dy---(1)$$ $$pressure=FA=MLT$$−$$2/L2=ML$$−$$1T$$−$$2$$ $$density=mass/volume=ML$$−$$3$$ $$velocity=LT$$−$$1$$ LT−$$1=(ML$$−$$1T$$−$$2)x$$. (ML$$−$$3)y$$ $$M0LT$$−$$1=Mx+y$$. L−x−$$3y$$. T−$$2x$$ compafring the powers of M,L,T M→$$x+y=0$$⇒         $$x=$$−y T→$$-2x=-1$$ ⇒$$x=12$$     ⇒$$y=-12$$ Substitute obtained values   in $$eqn(1)                                    $$v=p12$$   $$d-12$$

The velocity of sound in air $(v)$ pressure $(p)$ and density of air $(d)$ are related as $v α p^{x} d^{y}$ the value of $' x'$ and $' y'$ respectively are

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