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Question

The speed of sound in hydrogen gas at STP is vo. The speed of sound in a mixture containing 3 parts of hydrogen gas and 2 parts of oxygen gas at STP will be

A
vo3
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B
vo5
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C
vo6
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D
vo7
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Solution

The correct option is D vo√7At a given pressure and temperature, the density of gas is directly proportional to its molecular weight. PM=ρRT ⇒ρ∝M ⇒ρ1ρ2=M1M2=232=116 ⇒ρ2=16ρ1 ...............(1) Here, ρ1→ density of hydrogen, ρ2→ density of oxygen Now, density of mixture, ρmix=ρ1 V1 +ρ2 V2V1+V2 ⇒ρmix=ρ1V1+16ρ1×2V13V1+2V13=35ρ1 V15V1 [ given V1V2=32 and from (1)] ⇒ρmix=7 ρ1 ..........(2) Speed of sound, v=√γPρ At constant pressure, v∝1√ρ So, vH2vmix=√ρmixρH2 ⇒vmix=vH2×√ρH2ρmix ⇒vmix=vo×√ρ17ρ1 ⇒vmix=vo√7

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