Calculate the speed of sound in a liquid of density 2000 kg/m3 and bulk modulus 2 × 109 N/m2.500 m/s1000 m/s125 m/s250 m/s
Question
Calculate the speed of sound in a liquid of density 2000 kg/m³ and bulk modulus 2 × 10⁹ N/m².
Options:
- 500 m/s
- 1000 m/s
- 125 m/s
- 250 m/s
Solution
The speed of sound in a medium is given by the formula:
v = sqrt(B/ρ)
where: v is the speed of sound, B is the bulk modulus of the medium, and ρ is the density of the medium.
Given: B = 2 × 10^9 N/m^2 ρ = 2000 kg/m^3
Substituting these values into the formula, we get:
v = sqrt((2 × 10^9 N/m^2) / (2000 kg/m^3))
Solving this equation will give us the speed of sound in the liquid.
Let's calculate it:
v = sqrt((2 × 10^9) / 2000) v = sqrt(1 × 10^6) v = 1000 m/s
So, the speed of sound in the liquid is 1000 m/s.
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