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Question

According to Newton's formula, the speed of sound in air at STP is:
(Take the mass of $$1$$ mole of are is $$29 \times 10^{-3} \,\,kg)$$


A
250ms1
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B
260ms1
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C
270ms1
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D
280ms1
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Solution

The correct option is D $$280 \,\, m \,\,s^{-1}$$
$$1$$ mole of any gas occupies $$22.4$$ liters at STP.
Therefore, the density of air at STP is
$$\rho = \dfrac{\text{Mass of one mole of air}}{\text{Volume of one mole of air at STP}}$$
$$= \dfrac{29 \times 10^{-3} \,\,kg}{22.4 \times 10^{-3} \,\,m^3} = 1.29 \,\,kg \,\,m^{-3}$$
At STP, $$P = 1\,\,atm = 1.01 \times 10^5 \,\,N \,\,m^{-2}$$

$$V =\sqrt{\left( \dfrac { P }{ \rho  }\right)}=\sqrt { \dfrac {1.01 \times 10^5 \,\,N \,\,m^{-2}  }{ 1.29 \times kg \,\,m^{-3} }  } = 280 \,\,m \,\,s^{-1} $$

Physics

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