If the bulk modulus increases while density remains constant, the speed of sound will be

If the bulk modulus increases while density remains constant, the speed of sound will be

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

Answer: (A)

The key idea is how stiffness and density determine how quickly a disturbance moves through a medium. The speed of sound is related to the medium’s bulk modulus and its density, roughly c ≈ sqrt(B/ρ). If the density stays the same and the bulk modulus increases, the ratio B/ρ increases, so the speed of sound increases. In other words, the medium becomes stiffer and transmits sound more quickly. Therefore, the sound will travel faster. (If density increased instead while B stayed the same, the speed would decrease. If both B and ρ don’t change, the speed remains the same. It wouldn’t stop unless unrealistic conditions occur.)

The key idea is how stiffness and density determine how quickly a disturbance moves through a medium. The speed of sound is related to the medium’s bulk modulus and its density, roughly c ≈ sqrt(B/ρ). If the density stays the same and the bulk modulus increases, the ratio B/ρ increases, so the speed of sound increases. In other words, the medium becomes stiffer and transmits sound more quickly. Therefore, the sound will travel faster.

(If density increased instead while B stayed the same, the speed would decrease. If both B and ρ don’t change, the speed remains the same. It wouldn’t stop unless unrealistic conditions occur.)