The velocity of sound in air V- pressure P and density of air d are related as V - p x d y- The values of x and y respectively are

The correct option is C 1 2 , 1 2 v ∝ p^xd^y LT^ 1=(M^1L^ 1T^ 2)^x(ML^ 3)^y M^0L^1T^ 1=M^x+yL^ x 3yT^ 2x x+y=0 2 ...

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Standard XII

Physics

Newton's Contention

The velocity ...

Question

The velocity of sound in air (V), pressure ( P) and density of air ( d) are related as $V$ $α$ $p^{x} d^{y}$ . The values of x and y respectively are

1, \frac{1}{2}

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- \frac{1}{2}, - \frac{1}{2}

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\frac{1}{2}, \frac{1}{2}

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\frac{1}{2}, - \frac{1}{2}

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Solution

The correct option is C $\frac{1}{2}, - \frac{1}{2}$
$v$ $\propto$ $p^{x} d^{y}$
$L T^{- 1} = (M^{1} L^{- 1} T^{- 2})^{x} (M L^{- 3})^{y}$
$M^{0} L^{1} T^{- 1} = M^{x + y} L^{- x - 3 y} T^{- 2 x}$
$x + y = 0$
$- 2 x = - 1$ $\Rightarrow x = \frac{1}{2}$
$- x - 3 y = 1$
$y = - \frac{1}{2}$

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The velocity of sound in air (V), pressure ( P) and density of air ( d) are related as V α pxdy. The values of x and y respectively are

The correct option is C 12,−12v ∝ pxdyLT−1=(M1L−1T−2)x(ML−3)yM0L1T−1=Mx+yL−x−3yT−2xx+y=0−2x=−1 ⇒x=12−x−3y=1 y=−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 values of x and y respectively are

The correct option is C $\frac{1}{2}, - \frac{1}{2}$
$v$ $\propto$ $p^{x} d^{y}$
$L T^{- 1} = (M^{1} L^{- 1} T^{- 2})^{x} (M L^{- 3})^{y}$
$M^{0} L^{1} T^{- 1} = M^{x + y} L^{- x - 3 y} T^{- 2 x}$
$x + y = 0$
$- 2 x = - 1$ $\Rightarrow x = \frac{1}{2}$
$- x - 3 y = 1$
$y = - \frac{1}{2}$