Bulk ModulusGillian Trotter

What is Bulk Modulus?

• Bulk modulus tells us the compressibility of a fluid or solid[1,2]

• If something is highly compressible it has a low bulk modulus

• If something has low compressibility it has a high bulk modulus

• e.g. gases

Low Bulk Modulus

• Bulk modulus of air (20˚C) = 1.01 x 105 Pa[5]

Highly Compressibility

Low Compressibility

• e.g. Diamond (almost no compression)

High Bulk Modulus

• Bulk Modulus = 4.42 x 1011 Pa[5]

• Over 4 million times higher than that of air

Bulk Modulus Equation

B = -V • ∆p ∆V

V: the volume of the object

∆p: the change in pressure exerted on the material

∆V: the change in the volume of the object due to the pressure change

The “-” is due to the fact that the change in volume is ALWAYS opposite the sign of the change in pressure[2,5]

But why is the bulk modulus of an object important?

It helps us determine the

velocity of a wave

• v= √(Ts/μ)

• Ts is the tension (or stretchiness) of a string

• μ is the linear mass density

• v = √(B/ρ)

• B is the bulk modulus (or compressibility) of molecules

• ρ is the density of the object

Wave Speed on a String[5]

Wave Speed of Sound

The higher the bulk modulus, the faster the speed of sound

(in m/s).

Applications

The speed of sound is very significant in the process of animal echolocation, or

SONAR communication between animals.

Two examples of echolocation in two different mediums are: bats and whales.

Bats• Use echolocation to

detect how far away things are in the dark

• 1. A bat emits a high pitched frequency

• 2. The sound waves travel through the air until they hit a solid object (e.g. a cave wall)

• 3. The sound waves travel back to the bat

• 4. The bat can determine how far away the object is by the amount of time it takes for the sound to come back to them[3]

Bats are usually in close proximity to prey and other bats

They hunt in small spaces such as

caves, as well as the open air

Since they are not usually very far from objects or prey, it is

suitable that the bulk modulus of air is 1.01

x 105 Pa, and the speed of sound is 343

m/s[5]

Whales

• Air is moved in a whale’s sinuses[4], and a low frequency sound is emitted into the water

• Similar to bats, the time it takes for the sound wave to bounce off of an object and return to a whale helps determine how far away the object is

Certain species of whales have the ability to

communicate with each other via sound and song[4]

Whales use echolocation to communicate with other whales and detect prey

many kilometers away

Since whales are usually great distances from other pods (groups) of

whales, as well as prey or reefs, it is suitable that the bulk modulus of water is

2.2 x 109 Pa, and the speed of sound in water is 1,482

m/s[5]

Bibliography[1] Elasticity, Elastic Properties. Bulk Elastic Properties - http://hyperphysics.phy-astr.gsu.edu/hbase/permot3.html

[2] Aerodynamics For Students, 2005. Bulk Modulus - http://www-mdp.eng.cam.ac.uk/web/library/enginfo/aerothermal_dvd_only/aero/fprops/propsoffluids/node13.html

[3] Bat Conservation Trust, 2015. Echolocation - http://www.bats.org.uk/pages/echolocation.html

[4] Australian Government. Whales, Dolphins and Sound - http://www.environment.gov.au/marine/marine-species/cetaceans/whale-dolphins-sound

[5] Hawkes, R.; Iqbal, J.; Mansour, F.; Milner-Bolotin, M.; Williams, P. 2015. Physics for Scientists and Engineers, An Interactive Approach, Revised Custom Volume 1, Phys 101. Nelson Education Ltd. Toronto, Ontario