Bulk modulus measures the compressibility of a material. Materials with high bulk modulus like diamond have low compressibility, while gases have low bulk modulus and high compressibility. Bulk modulus helps determine the speed of sound in a medium, with higher bulk modulus corresponding to higher sound speed. This relationship allows bats and whales to use echolocation - emitting sounds and interpreting echoes - to navigate and find prey over varying distances depending on the bulk modulus of the medium (air vs. water).

1. Bulk Modulus
Gillian Trotter

2. 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

3. • e.g. gases
Low Bulk Modulus
• Bulk modulus of air
(20˚C) = 1.01 x 105 Pa[5]
Highly Compressibility

4. 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

5. 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]

6. But why is the
bulk modulus of
an object
important?

7. 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

8. The higher the bulk
modulus, the faster
the speed of sound (in
m/s).

9. 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.

10. 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]

11. 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]

12. 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

13. 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]

14. 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/fp
rops/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