golgi wrote:Hello, this was a question in a Next Step test.
Which of the following properties explains why sound wave velocity increases as it travels from air to a liquid medium at the same temperature?
A. Kinetic energy of the medium
B. Volume of the medium
C. Density of the medium
D. Bulk modulus of the medium
The credited answer is D, because of the equation v = √(Κ/ρ) where K is bulk modulus and ρ is density. It is said that C is wrong because density has an inverse relationship with sound wave velocity.
However, I feel like both C & D would be good answers due to the way the question is worded. I don't see where it asks about a positive relationship..
Hello golgi,
I'm not sure exactly what you mean by "I don't see where it asks about a positive relationship" but I will try to answer why C is not correct.
The question tells us (and we should already know) that sound wave velocity is higher in solids then liquids then gases. With the equation v = √(Κ/ρ) we can see that as density (ρ) increases, the wave velocity (v) will decrease--an inverse relationship. So if we are going from air to liquid (i.e. where the density is higher) we expect the wave velocity to decrease. The density increase is responsible for a DECREASE in velocity so Choice C cannot be correct as this does not explain the increase in velocity.
But, as stated above, we know velocity is higher in liquid compared to gas, so it must be that the bulk modulus increase that is overcoming the decrease in velocity created by the density increase. The higher bulk modulus of liquids is responsible for the INCREASE in velocity, so D is correct.
Hope this clears it up!