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  4. When a certain volume of water is subjected to 100kPa pressure, the volume of water decreases by 0.005%. The speed of sound in water must be

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Q. When a certain volume of water is subjected to 100kPa pressure, the volume of water decreases by 0.005%. The speed of sound in water must be

MGIMS WardhaMGIMS Wardha 2009

Solution:

Bulk modulus $ K=\frac{\Delta p}{\frac{\Delta V}{V}}=\frac{100\times {{10}^{3}}}{0.005/100}=2\times {{10}^{9}}Pa $ Speed $ v=\sqrt{\frac{K}{d}}=\sqrt{\frac{2\times {{10}^{9}}}{{{10}^{3}}}}=\sqrt{2}\times {{10}^{3}} $ $ \Rightarrow $ $ v=1.400\times {{10}^{3}}=1400\,m/s $