lo4 - sound waves

• Sound waves are longitudinal waves – the direction of travel of

particles is parallel to the direction of propagation

Compression

High pressure Rarefaction

Low pressure

• On a pressure-direction of travel graph, rarefactions

occur at troughs and compressions occur at crests.

Pressure

Direction of Travel

SO WHAT IS THE RELATIONSHIP BETWEEN

DISPLACEMENT AND PRESSURE??

• Consider a sound

wave of single

frequency

• The displacement

and pressure

graphs are shown

on the right

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

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

• 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

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

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?

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

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.

THANKS FOR WATCHING :]

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]

LINK

http://www.slideshare.net/celesteng505/lo4-sound-waves