How does speed change when bulk modulus increases?

How does speed change when bulk modulus increases?

• A. Slower
• B. Unchanged
• C. Faster
• D. Dramatically Slower

Answer: (C)

Increasing bulk modulus means the medium is stiffer and resists compression more. When a pressure disturbance travels, a stiffer medium transmits that disturbance to neighboring particles more quickly, so the wave propagates faster. In fluids, the speed of sound is v = sqrt(B/ρ). If the bulk modulus B goes up while density ρ stays roughly the same, v increases as the square root of B. In solids, longitudinal wave speed is v = sqrt((K + 4/3 μ)/ρ), where K is the bulk modulus and μ is the shear modulus. Raising K raises the numerator, boosting speed (though μ also plays a role). Either way, a higher bulk modulus tends to produce a faster wave, so the correct interpretation is that the speed increases.

Increasing bulk modulus means the medium is stiffer and resists compression more. When a pressure disturbance travels, a stiffer medium transmits that disturbance to neighboring particles more quickly, so the wave propagates faster.

In fluids, the speed of sound is v = sqrt(B/ρ). If the bulk modulus B goes up while density ρ stays roughly the same, v increases as the square root of B. In solids, longitudinal wave speed is v = sqrt((K + 4/3 μ)/ρ), where K is the bulk modulus and μ is the shear modulus. Raising K raises the numerator, boosting speed (though μ also plays a role). Either way, a higher bulk modulus tends to produce a faster wave, so the correct interpretation is that the speed increases.