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A liquid with specific gravity of 0.94 undergoes a reduction in volume of 0.22% when subjected to an increase in pressure of 1400kPa. The velocity of propagation of sound in this liquid will be ___________m/s
- a)822.55
- b)922.55
- c)1022.55
- d)1122.55
Correct answer is option 'A'. Can you explain this answer?
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Solution:
Given data:
Specific gravity of liquid (S) = 0.94
Reduction in volume (ΔV/V) = 0.22%
Increase in pressure (ΔP) = 1400 kPa
To find: Velocity of propagation of sound in the liquid (v)
Formula used:
Bulk modulus of elasticity (K) = -V(ΔP/ΔV)
Velocity of propagation of sound (v) = √(K/ρ)
where, ρ is the density of the liquid.
Calculation:
Density of the liquid can be calculated as:
ρ = S × ρ_w
where, ρ_w is the density of water.
ρ_w = 1000 kg/m³
ρ = 0.94 × 1000 = 940 kg/m³
Bulk modulus of elasticity can be calculated as:
K = -V(ΔP/ΔV)
Here, we have ΔV/V = 0.22%
So, ΔV = (ΔV/V) × V = (0.22/100) × V
where, V is the initial volume of the liquid.
Therefore, K = -V(ΔP/ΔV) = -V(1400×10³)/(0.22/100) × V)
K = -6.36×10¹⁰ Pa
Velocity of propagation of sound can be calculated as:
v = √(K/ρ) = √((-6.36×10¹⁰)/940) = 822.55 m/s
Therefore, the velocity of propagation of sound in the given liquid is 822.55 m/s.
Hence, option (a) is the correct answer.
Given data:
Specific gravity of liquid (S) = 0.94
Reduction in volume (ΔV/V) = 0.22%
Increase in pressure (ΔP) = 1400 kPa
To find: Velocity of propagation of sound in the liquid (v)
Formula used:
Bulk modulus of elasticity (K) = -V(ΔP/ΔV)
Velocity of propagation of sound (v) = √(K/ρ)
where, ρ is the density of the liquid.
Calculation:
Density of the liquid can be calculated as:
ρ = S × ρ_w
where, ρ_w is the density of water.
ρ_w = 1000 kg/m³
ρ = 0.94 × 1000 = 940 kg/m³
Bulk modulus of elasticity can be calculated as:
K = -V(ΔP/ΔV)
Here, we have ΔV/V = 0.22%
So, ΔV = (ΔV/V) × V = (0.22/100) × V
where, V is the initial volume of the liquid.
Therefore, K = -V(ΔP/ΔV) = -V(1400×10³)/(0.22/100) × V)
K = -6.36×10¹⁰ Pa
Velocity of propagation of sound can be calculated as:
v = √(K/ρ) = √((-6.36×10¹⁰)/940) = 822.55 m/s
Therefore, the velocity of propagation of sound in the given liquid is 822.55 m/s.
Hence, option (a) is the correct answer.
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A liquid with specific gravity of 0.94 undergoes a reduction in volume of 0.22% when subjected to an increase in pressure of 1400kPa. The velocity of propagation of sound in this liquid will be ___________m/sa)822.55b)922.55c)1022.55d)1122.55Correct answer is option 'A'. Can you explain this answer?
Question Description
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A liquid with specific gravity of 0.94 undergoes a reduction in volume of 0.22% when subjected to an increase in pressure of 1400kPa. The velocity of propagation of sound in this liquid will be ___________m/sa)822.55b)922.55c)1022.55d)1122.55Correct answer is option 'A'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A liquid with specific gravity of 0.94 undergoes a reduction in volume of 0.22% when subjected to an increase in pressure of 1400kPa. The velocity of propagation of sound in this liquid will be ___________m/sa)822.55b)922.55c)1022.55d)1122.55Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A liquid with specific gravity of 0.94 undergoes a reduction in volume of 0.22% when subjected to an increase in pressure of 1400kPa. The velocity of propagation of sound in this liquid will be ___________m/sa)822.55b)922.55c)1022.55d)1122.55Correct answer is option 'A'. Can you explain this answer?.
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