Sound

and the Doppler effectand the Doppler effect

L7 c1

In general the velocity of a wave is

a. f/T T=tension

b. λ/T T=period

c. 2π/ω

d. 2π/k

e. ωt

SoundSound waves

represent compressions and rarefactions of the

medium

This can be the surface of a

speaker, or your vocal chords

x

Density

or P

The higer the pressure the

faster the speed of the waves

The denser a medium is the

slower the speed of the

waves

v must grow with P

v must drop with

• P has units of force/area: mass/(length • time2)• has units of mass /length3

The only combination that has units of speed is:

P

cv These arguments determine

v up to a numerical constant c.

Its value depends on the medium

13.25

• A sinusoidal sound wave is described by the displacement

D(x,t)=(2m)cos[(15.7m-1)x-(858s-1)t]a) find the amplitude, wavelength and speed of

this waveb) Determine the instantaneous displacement of

an element of air at the position x=0.5 m at t=3ms

c) Determine the maximum speed of an elements oscillatory motion

Exercise 13.25 I need the general expression for a wave. The rest is plug and chug

-1 -1

sin( )

(2 m)cos 15.7 m 858 s

D A kx t

x t

-1

( ) 2 m = /2

2 2 15.7m m 0.4m

15.7858 m m

54.6515.7 s s

a A

k

vk

( ) x 0.05m, 0.003s

(2 m)cos 15.7 0.05 858 0.003

1.95 m

b t

D

-1( ) A cos( ) A 858 s (2 m) 0.0017m/sdD

c kx tdt

remembercos=sin(+/2)

L7 c2) All mechanical waves require

a. some source of disturbance.

b. a medium that can be disturbed.

c. a physical mechanism through which particles of the medium can exert forces on one another.

d. all of the above.

e. only (a) and (b) above.

The Doppler effect

• Passing Train

• Doppler applet

• Doppler2

General Doppler Formula

LL S

S

v vf f

v v

fs= frequency emitted by source vS=Velocity of source

fL= frequency received by listener vL=Velocity of listener

positive direction is from L to S so fL>fS when they are moving toward each other

SSourceLListener

+

vs (negative) vL (positive)

• L7 C3) The Doppler effect causes the sound from a source moving toward an observer to appear to have a

a. greater amplitude.

b. smaller amplitude.

c. greater speed.

d. lower frequency.

e. higher frequency.

Example

Example: Police car w/ siren and passenger car approaching each other; both moving.fsiren = 250 Hz vs = 27 m/s (60 mph) vL = 27 m/s

f (250)330 27

330 27

295 Hz

Once they pass each other and are moving away

f (250)330 27330 27

213 Hz

LL S

S

v vf f

v v

fs= frequency emitted by source vS=Velocity of source

fL= frequency received by listener vL=Velocity of listener

positive direction is from L to S so fL>fS when they are moving toward each other

Ultrasound

f=3Hz water~0.5 mm

10 wks

2

12

F=-kx x=Acos( t+ )

1

2spring

f fT

kSHO

m

gPendulum

L

PE kx Energy PE KE

total 0

0

2 2 2 20

2 20

sin( )

/

( / ) ( )

/tan

ma F kx bv F t

F mA

b m

b m

2

)2/(

2

)cos(

m

b

m

k

tAex tmb

/0

t mE E e where

b

( , ) sin( )

2

D x t A kx t

k vk

dampled SHO

driven and dampled SHO

traveling waves

2 2

2 2 2

1d d

dt c dx

E E

8

0 0

13 10 m/sc

0

0

0 0

cos( )

cos( )

E kx t

B kx t

E cB

E x

B z

^

^

2av 0 0

1

2u E

0

1S E B

2

0 0

~ /EB E

Power areac

S

20

02avg

EPowerI S

Area c p=E/c

1 1 / 1 PowerP

F p E c I

A A t A t A c c

I=I0 cos2

LL S

S

v vf f

v v

positive direction is from L to S