Lecture 29

General Physics (PHY 2130)

http://www.physics.wayne.edu/~apetrov/PHY2130/

•  Sound   Intensity of sound waves   Doppler’s effect

•  Thermal physics   Zeroth law of thermodynamics, temperature   Thermal expansion

Lightning Review

Last lecture: 1.  Sound

  sound waves, generation   standing sound waves. Musical instruments.

Review Problem: Imagine holding two identical bricks under water. Brick A is just beneath the surface of the water, while brick B is at a greater depth. The force needed to hold brick B in place is

1. larger 2. the same as 3. smaller

than the force required to hold brick A in place.

3

The Human Ear

Intensity of Sound Waves • The intensity of a wave is the rate at which the energy flows through a unit area, A, oriented perpendicular to the direction of travel of the wave

• P is the power, the rate of energy transfer • Recall that units are W/m2

AP

tAEI =Δ

Δ=

Various Intensities of Sound

•  Threshold of hearing •  Faintest sound most humans can hear •  About 1 x 10-12 W/m2

•  Threshold of pain •  Loudest sound most humans can tolerate •  About 1 W/m2

•  The ear is a very sensitive detector of sound waves

Intensity Level of Sound Waves

• The sensation of loudness is logarithmic in the human hear

• β is the intensity level or the decibel level of the sound

•  Io is the threshold of hearing •  Threshold of hearing is 0 dB •  Threshold of pain is 120 dB •  Jet airplanes are about 150 dB

oIIlog10=β

Example: rock concert

The sound intensity at a rock concert is known to be about 1 W/m2. How many decibels is that?

… and who is this guy?

Example:

Given: I0=10-12 W/m2

I1=100 W/m2

Find: 1.  β=?

1. Use a definition of intensity level in decibels:

( ) dB

II

12010log101010log10

log10

121012

0

10

010

==⎟⎟⎠

⎞⎜⎜⎝

⎛=

=⎟⎟⎠

⎞⎜⎜⎝

⎛=

−

β

 

Note: same level of intensity level as pain threshold! Normal conversation’s intensity level is about 50 dB.

The guy is Klaus Meine (Scorpions)

Doppler Effect • A Doppler effect is experienced whenever there is relative motion between a source of waves and an observer. • When the source and the observer are moving toward

each other, the observer hears a higher frequency • When the source and the observer are moving away

from each other, the observer hears a lower frequency • Although the Doppler Effect is commonly experienced with sound waves, it is a phenomena common to all waves

Doppler Effect, Observer Moving

⎟⎠

⎞⎜⎝

⎛ +=

vvv oƒƒ'

Doppler Effect, Observer Moving • The apparent frequency, ƒ’, depends on the actual frequency of the sound and the speeds

• vo is positive if the observer is moving toward the source and negative if the observer is moving away from the source

⎟⎠

⎞⎜⎝

⎛ +=

vvv oƒƒ'

Doppler Effect, Source Moving

• Use the –vs when the source is moving toward the observer and +vs when the source is moving away from the observer

⎟⎟⎠

⎞⎜⎜⎝

⎛

−=

svvvƒƒ'

Doppler Effect, both moving • Both the source and the observer could be moving

• Use positive values of vo and vs if the motion is toward •  Frequency appears higher

• Use negative values of vo and vs if the motion is away •  Frequency appears lower

⎟⎟⎠

⎞⎜⎜⎝

⎛

−

+=

s

o

vvvvƒƒ'

Example: taking a train

An alert phys 2130 student stands beside the tracks as a train rolls slowly past. He notes that the frequency of the train whistle is 442 Hz when the train is approaching him and 441 Hz when the train is receding from him. From this he can find the speed of the train. What value does he find?

Example:

Given: frequencies:

f1=442 Hz f2=441 Hz

sound speed: v=345 m/s Find: v=?

 

With the train approaching at speed , the observed frequency is

(1) As the train recedes, the observed frequency is

(2) Dividing equation (1) by (2) gives , and solving for the speed of the train yields

345 m s 0 345 m s442 Hz345 m s 345 m st t

f fv v

⎛ ⎞ ⎛ ⎞+= =⎜ ⎟ ⎜ ⎟

− −⎝ ⎠ ⎝ ⎠

( )345 m s 0 345 m s441 Hz

345 m s 345 m st tf f

v v⎡ ⎤ ⎛ ⎞+

= =⎢ ⎥ ⎜ ⎟− − +⎝ ⎠⎣ ⎦

345 m s442441 345 m s

t

t

vv

+=

−

tv = 0.391 m s

16

o

s

28 m s343 m s

o s 44 m s343 m s

11(550 Hz) 580 Hz

11

vvvv

f f−−

= = =−−

Example: An ambulance traveling at 44 m/s approaches a car heading in the same direction at a speed of 28 m/s. The ambulance driver has a siren sounding at 550 Hz. At what frequency does the driver of the car hear the siren?

This is a Doppler effect problem with both source and observer moving:

17

Sound waves can be sent out from a transmitter of some sort; they will reflect off any objects they encounter and can be received back at their source. The time interval between emission and reception can be used to build up a picture of the scene.

Echolocation

18

Example: A boat is using sonar to detect the bottom of a freshwater lake. If the echo from a sonar signal is heard 0.540 s after it is emitted, how deep is the lake? Assume the lake’s temperature is uniform and at 25 °C.

The signal travels two times the depth of the lake so the one-way travel time is 0.270 s. From table 12.1, the speed of sound in freshwater is 1493 m/s.

( )( ) m 403s 270.0m/s 1493depth

==

Δ= tv

Thermal Physics

20

Heat is the flow of energy due to a temperature difference. Heat always flows from objects at high temperature to objects at low temperature.

When two objects have the same temperature, they are in thermal equilibrium.

Zeroth law of thermodynamics

If objects A and B are separately in thermal equilibrium with a third object C, then A and B are in thermal equilibrium with each other.

Allows to introduce temperature.

Temperature Scales

•  Thermometers can be calibrated by placing them in thermal contact with an environment that remains at constant temperature •  Environment could be mixture of ice and water in thermal equilibrium •  Also commonly used is water and steam in thermal equilibrium

Celsius Scale

•  Temperature of an ice-water mixture is defined as 0º C •  This is the freezing point of water

•  Temperature of a water-steam mixture is defined as 100º C •  This is the boiling point of water

• Distance between these points is divided into 100 segments

Kelvin Scale

• When the pressure of a gas goes to zero, its temperature is –273.15º C

•  This temperature is called absolute zero •  This is the zero point of the Kelvin scale

•  –273.15º C = 0 K

•  To convert: TC = TK – 273.15

Some Kelvin Temperatures

• Some representative Kelvin temperatures

• Note, this scale is logarithmic

• Absolute zero has never been reached

Fahrenheit Scale

• Most common scale used in the US •  Temperature of the freezing point is 32º •  Temperature of the boiling point is 212º •  180 divisions between the points

Comparing Temperature Scales

273.159 32595

C K

F C

F C

T T

T T

T T

= −

= +

Δ = Δ

28

Example: On a warm summer day, the air temperature is 84°F. Express this temperature in (a) °C and (b) kelvins.

( )

CF/8.1F32

F32CF/ 8.1

00

0F

C

CF

−=

°+°°=

TT

TT

273.15C +=TT

Fahrenheit/Celsius

Absolute/Celsius

Thermal Expansion

• The thermal expansion of an object is a consequence of the change in the average separation between its constituent atoms or molecules

• At ordinary temperatures, molecules vibrate with a small amplitude

• As temperature increases, the amplitude increases •  This causes the overall object as a whole to expand

Linear (area, volume) Expansion

•  For small changes in temperature

•  The coefficient of linear expansion, , depends on the material

•  Similar in two dimensions (area expansion)

• … and in three dimensions (volume expansion)

tLL o Δ=Δ αα

αγγ 2, =Δ=Δ tAA o

αββ 3,solidsfor =Δ=Δ tVV o

31

Expansion joints permit the roadbed of a bridge to expand and contract as the temperature changes

Example

A copper telephone wire has essentially no sag between poles 35.0 m apart on a winter day when the temperature is –20.0°C. How much longer is the wire on a summer day when TC = 35.0°C? Assume that the thermal coefficient of copper is constant throughout this range at its room temperature value.

Applications of Thermal Expansion

1. Thermostats •  Use a bimetallic strip •  Two metals expand differently

2. Pyrex Glass •  Thermal stresses are smaller than for ordinary glass

3. Sea levels •  Warming the oceans will increase the volume of the oceans

34

Example: A highway is made of concrete slabs that are 15 m long at 20.0°C. (a) If the temperature range at the location of the highway is from –20.0°C to +40.0°C, what size expansion gap should be left (at 20.0°C) to prevent buckling of the highway? (b) How large are the gaps at –20.0°C?