If the density doubles while the bulk modulus remains the same, how does the speed of sound change?

If the density doubles while the bulk modulus remains the same, how does the speed of sound change?

• A. It remains unchanged
• B. It decreases by a factor of sqrt(2)
• C. It increases
• D. It becomes zero

Answer: (B)

The speed of sound in a medium depends on how stiff the medium is to compression relative to how much inertia it has, described by c = sqrt(B/ρ), where B is the bulk modulus and ρ is the density. If the density doubles while the bulk modulus stays the same, the speed becomes c' = sqrt(B/(2ρ)) = (1/√2) sqrt(B/ρ) = c/√2. So the speed decreases by a factor of √2. Intuitively, more mass to move means more inertia for the wave to overcome, while the stiffness resisting compression hasn’t changed, leading to slower sound propagation.

The speed of sound in a medium depends on how stiff the medium is to compression relative to how much inertia it has, described by c = sqrt(B/ρ), where B is the bulk modulus and ρ is the density. If the density doubles while the bulk modulus stays the same, the speed becomes c' = sqrt(B/(2ρ)) = (1/√2) sqrt(B/ρ) = c/√2. So the speed decreases by a factor of √2. Intuitively, more mass to move means more inertia for the wave to overcome, while the stiffness resisting compression hasn’t changed, leading to slower sound propagation.