An increase of pressure by 100 kPa decreases the volume of water by 5 × 10⁻³% of its original volume. Find the speed of sound in water if ρ = 10³ kg m⁻³.
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An increase of pressure by 100 kPa decreases the volume of water by 5 × 10⁻³% of its original volume. Find the speed of sound in water if ρ = 10³ kg m⁻³.

G1 Physics · Accepted Answer

Step 1: Volume strain = 5×10⁻³% = 5×10⁻⁵. Step 2: Bulk modulus B = ΔP/(ΔV/V) = 10⁵/(5×10⁻⁵)=2×10⁹ Pa. Step 3: v = √(B/ρ)=√(2×10⁹/10³)=√(2×10⁶)≈1414 m s⁻¹. Final: B.