The speed of sound in oxygen (O₂) at a certain temperature is 460 ms⁻¹. The speed of sound in helium (He) at the same temperature will be (assumed both gases to be ideal)

1420 ms⁻¹

550 ms⁻¹

375 ms⁻¹

650 ms⁻¹

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Solution

1420 ms⁻¹

straight v equals space square root of fraction numerator straight gamma space RT over denominator straight M end fraction end root fraction numerator straight V subscript 1 over denominator space straight V subscript 2 end fraction space equals space square root of fraction numerator straight gamma subscript 1 straight M subscript 2 over denominator straight gamma subscript 2 straight M subscript 1 end fraction end root space equals space square root of fraction numerator begin display style 7 over 5 end style straight x 4 over denominator begin display style 5 over 3 end style straight x 32 end fraction end root 460 over straight V subscript 2 space equals space square root of fraction numerator 21 over denominator 25 space straight x 8 end fraction end root rightwards double arrow space straight v subscript 2 space space equals space fraction numerator 460 space straight x space 5 space straight x space 2 square root of 2 over denominator square root of 21 end fraction space equals 1420 space ms to the power of negative 1 end exponent

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