This powerpoint presentation looks at some properties of sound waves and explains the relationship between displacement and pressure of sound waves with a practice problem at the end.
2. • Sound waves are longitudinal waves – the direction of travel of
particles is parallel to the direction of propagation
Compression
High pressure Rarefaction
Low pressure
3. • On a pressure-direction of travel graph, rarefactions
occur at troughs and compressions occur at crests.
Pressure
Direction of Travel
4. SO WHAT IS THE RELATIONSHIP BETWEEN
DISPLACEMENT AND PRESSURE??
5. • Consider a sound
wave of single
frequency
• The displacement
and pressure
graphs are shown
on the right
6. A FEW OBSERVATIONS
• When the displacement is
at the equilibrium position
(y = 0), the pressure is at
its highest
• When the displacement is
the greatest (y = 10), the
pressure is 0
7. WHY???
• When the pressure is high (at compressions), particles are
pushed into the area from both left and right
• Displacement is positive on the right and negative on the left
• This occurs when the particle passes through zero, where the
pressure is maximized
8. • When the pressure is low (at rarefactions), particles
moves away on both left and right
• Particle in the area is stationary and can move left or right
• This happens when the displacement is at its crest or
trough
9. RECAP…
• When the displacement is at its greatest, pressure is zero
• When the displacement is zero, pressure is at its greatest.
• If the displacement follows a sine function, the pressure
changes like a cosine function
• i.e. displacement and pressure are π/2 radians out of phase
Displacement
Pressure
Π/2
rad
10. FOOD FOR THOUGHT
Question: Imagine an alien from a planet called Pressurnet
came to visit Earth. You wanted to approach the alien but
he is sensitive to pressure changes. He is standing
10.378 meters away from you when you decided to call
out to him. The displacement amplitude of the your sound
(as it reached the alien) is 0.3405 μm and the frequency is
1000 Hz. [assume the displacement follows a sine
function]
a. What is the pressure of your voice as it reaches the
alien?
b. If the alien runs away when it is subjected to pressure
higher than 0.5 mPa, will he run away when you call out
to him?
11. Using equation 15-11 on page 427 of the textbook,
• Δpm = Bksm
• B = 1.01 x 105 Pa
• k = 2*π/λ =2*π*f/v (since v = f*λ, i.e. λ = v/f)
• Therefore,
• Δpm = (B*2*π*f*sm)/v
• = (1.01 x 105 Pa * 2 * π *1000 * 0.3405 μm)/(343 m/s)
• = 0.00063 Pa = 0.63 mPa
12. WRAPPING UP…
a. The pressure of the sound as it reaches the alien is
approximately 0.63 mPa.
a. Since 0.63 mPa > 0.5 mPa, the alien will run away when
you call out to him.
14. REFERENCES
Hawks, R., Iqbal, J., Mansour, F., Milner-Bolotin, M., & Williams P. 2014. Physics
for Scientists and Engineers: An Interactive Approach (1st ed.) Nelson.
Nave, R. Sound. HyperPhysics. Retrieved from http://hyperphysics.phy-
astr.gsu.edu/hbase/sound/tralon.html [accessed 20 Feb 2015]
Sound Reflection. 2014. TutorVista. Retrieved from
http://physics.tutorvista.com/waves/sound-reflection.html [accessed 20 Feb
2015]
