Types of Traveling Waves

• Transverse wave – the displacement of the wave is perpendicular to the motion of the wave– Sine and cosine graphs– Light waves (electromagnetic waves)

• Longitudinal wave – the displacement of the wave is parallel to the motion of the wave– Sound waves

Transverse Wave

Longitudinal Wave

Closer look at a Transverse Wave

Plots of the position

• y vs. x plot – provides information about the wavelength of the wave

• y vs. t plot – provides information about the period of the motion of the wave

Equations of Motion

vtxAtxy

2

sin),(

tkxAtxy sin),(

Tv

2

k

T

2

Equations of Motion (cont.)

tkxAtxv cos),(

tkxAtxa sin),( 2

AvMAX

AaMAX2

Properties of the string

• Linear mass density:

• Wave speed:

l

m

IMPORTANT

• There are two different velocities for a traveling transverse wave. – The wave velocity, which is literally how fast

the wave is moving to the left or to the right.

– The transverse velocity, which is how fast the wave (rope, string) is moving up and down.

Energy in a Traveling Wave

22

41 AU

2241 AK

22

2122

4122

41 AAAKUE

vAT

A

T

E

t

E 2221

2221

Sound•Sound waves are

–Longitudinal –Pressure Waves

•Infrasonic – less than 20 Hz•Audible – between 20 and 20,000 Hz•Ultrasonic – greater than 20,000 Hz

•Frequency – tone•Amplitude – volume

• Sound waves are mechanical waves, which means the wave needs a medium to travel through. (This is why there is no sound in space, there is no air for the sound wave to propagate through)

• Sound waves are traveling pressure waves. They are packets of low and high pressure regions which are picked up by your eardrums and interpreted as sounds in your brain.

Speed of Sound

• In air (at 20 oC) = 343 m/s

• In air (T in Kelvin)

K

Tsmv273

)/331(

Speed of Sound

• In a fluid or gas - depends on the density of the medium and the Bulk Modulus (ch. 9)

• In a solid - depends on the density of the medium and the Young’s Modulus (ch. 9)

B

v

Y

v

Power in a sound wave

Previously, we calculated the power (the rate of energy transfer) in a wave traveling on a string. In the same way, we can calculate the power in a sound wave as it propagates through a medium.

• Energy in one wavelength:

• Power in one wavelength:

2

max21 sAE

vsAT

sA

T

sA

T

E

t

E

2max2

12max2

1

2max2

1

Intensity of Sound

Another important property of sound waves is the intensity.

• The intensity of a wave is defined as the rate at which energy flows through a surface area – the power per unit area.

vsA

vsA

AI 2

max21

2max2

1

Intensity of Sound (cont.)

We can also write the intensity in terms of the pressure of the sound wave:

This equation for intensity is more practical in experimental applications because and v are properties of the medium, therefore they are easier to determine in an experiment than and smax which are properties of the sound wave.

v

PsPI

svP

2

2max

maxmax21

maxmax

Decibel Level

• Because our hearing covers a frequency range of 20 - 20,000 Hz, it’s often easier to talk about sound intensity in terms of decibels (dB).

Io=1.0 x 10-12 W/m2

(this is the reference intensity – the sound intensity at the threshold of hearing)

oI

Ilog10

Spherical and Plane Waves

• Sound waves are spherical waves – they move away from a source in all directions.

• But if you’re close to the source, the waves look (and act) as though they’re plane waves.

Multiple Sources of Sound

• If there are two or more sound sources, the total intensity of the sound you hear is the sum of the intensity of each individual sound wave.

Doppler Effect

• Because sound waves are spherical waves, your position and motion (relative to the source of the sound) will affect what you hear. This effect is called the Doppler Effect.

• If neither the source nor the observer are moving, then the sound heard by the observer will not be altered.

• But if either the source or the observer (or both) are moving relative to each other, then there will be a Doppler shift in the frequency (tone) of the sound.