The speed of sound in oxygen -O-2- nbsp-at a certain temperature is 460-m-s- nbsp- The speed in helium -He- at the same temperature will be -assume both gases to be ideal-460-m-s500-m-s650-m-s1420-m-s

The correct option is D 1420 m/sSpeed of sound is given by V=√(γ RTM) As γ _O_2 =75,M_O_2 =32 nbsp; and γ _He =53,M_He =4 nbsp; V_O_2 =√(75RT32) and V_He ...

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Standard XII

Physics

Derivation of the Speed of Sound

The speed of ...

Question

The speed of sound in oxygen $(O_{2})$ at a certain temperature is $460 m / s$ . The speed in helium $(H e)$ at the same temperature will be [assume both gases to be ideal]

460 m / s

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500 m / s

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650 m / s

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1420 m / s

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Solution

The correct option is D $1420 m / s$
Speed of sound is given by $V = \sqrt{\frac{γ R T}{M}}$

As
$γ_{O_{2}} = \frac{7}{5}, M_{O_{2}} = 32$ and $γ_{H e} = \frac{5}{3}, M_{H e} = 4$

$V_{O_{2}} = \sqrt{\frac{\frac{7}{5} R T}{32}}$ and
$V_{H e} = \sqrt{\frac{\frac{5}{3} R T}{4}}$

$\frac{V_{O_{2}}}{V_{H e}} = \sqrt{\frac{7 \times 3 \times 4}{5 \times 5 \times 32}}$

$V_{H e} = 460 \times 10 \times \sqrt{\frac{2}{21}} = 1420 m / s$

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The speed of sound in oxygen (O2) at a certain temperature is 460 m/s. The speed in helium (He) at the same temperature will be [assume both gases to be ideal]

The correct option is D 1420 m/sSpeed of sound is given by V=√γRTM As γO2=75,MO2=32 and γHe=53,MHe=4 VO2= ⎷75RT32 and VHe= ⎷53RT4 VO2VHe=√7×3×45×5×32 VHe=460×10×√221=1420 m/s

The speed of sound in oxygen $(O_{2})$ at a certain temperature is $460 m / s$ . The speed in helium $(H e)$ at the same temperature will be [assume both gases to be ideal]