physics 2111 unit 24 - college of dupagesound is longitudinal wave - media oscillates back and forth...

Physics 2111

Unit 24

Today’s Concepts:A) Sound waves

B) Interference

C) Intensity and Intensity Level

D) Doppler Effect

E) Beats

Mechanics Lecture 24, Slide 1

Sound is longitudinal wave - media oscillates back and forth in the

direction of travel of the wave

Sound Waves


direction of travel

direction of oscillations

So what the heck am I plotting when I show a sound wave like this?

Value of longitudinal displacement! (back and forth, not up and down.)

x

Recall that if I have two waves that a half of wave length out of phase, I get

destructive interference

Interference


l/2

No sound - silence


How do I get them out of phase like that?

Start in phase….

Both waves

maximum at

your ear

but travel different distance to receiver

One maximum,

one minimum at

your ear

DL


L1

L2

L1

L2

L1-L2 = DLDL = l *1, 2, 3, 4... constructive

DL = l *1/2, 3/2, 5/2... destructive

Example 24.1 (Two Speakers)


A 214 Hz tone is emitted from

two stereo speakers, 3.2

meters apart. Alex stands 2.4

meters in front the right

speaker. The speed of sound

in the surrounding air is

343m/sec. Does he hear a

loud or a soft tone?

3.2m

2.4m

Question


A 214 Hz tone is emitted from

two stereo speakers, 3.2

meters apart. Alex stands 2.4

meters in front the right

speaker. Does he hear a loud

or a soft tone?

3.2m

2.4m

A) Loud

B) Soft

C) We can’t tell yet

Example 24.2 (Two Different Speakers)


A varying tone is emitted from two

stereo speakers, 2m meters

apart. Augie stands 3.45 meters

in front the right speaker. The

speed of sound in the sounding

air is 343m/sec. What are the first

two frequencies above 800Hz for

which he hears completely

constructive interference?

Completely destructive

interference?

2m

3.45m

Question: Interference


A tone of varying frequency is emitted

from two stereo speakers, 2.4 meters

apart. Our hero stands 15 meters in

front the right speaker.

If the tone starts at 2000Hz and

increases what is the first frequency for

which he will hear the loudest sound?

2.4m

15m



What is the difference in the distance

the two sound waves traveled?

A) 2.4m

B) 15m

C) 0.25m

D) 0.21m

E) 0.19m

2.4m

15m



To here a loud sound, what should the

difference in the distance the two sound

waves traveled be in terms of wave

lengths?

A) n*l

B) l*(n+1/2)

C) l/n

D) l/(n+1/2)

E) n/l

2.4m

15m



What is our relationship between

wavelength(l), frequency(f) and velocity

of the wave (v)?

A) f = v*l

B) f = l/v

C) v = l/f

D) v =f*l

E) v = f/l

2.4m

15m



Set the difference in the distance

traveled to the requirement for

constructive interference. Use the

relationship between v, f and l just

found. You get what formula?

A) f = n*v/DL

B) f= n*v*DL

C) f = (n+1/2)*v/DL

D) f = (n+1/2)*v*DL

2.4m

15m



Take the value for DX we calculated and

the formula we just derived. Plug in

different values of m. What is the

lowest frequency you get above

2000Hz that will have constructive

interference? (vsound = 343m/sec)

A) 2520Hz

B) 3610Hz

C) 3810Hz

D) 4000Hz

2.4m

15m



Take the value for DX we calculated and

the formula we just derived. Plug in

different values of m. What is the

lowest frequency you get above

2000Hz that will have destructive

interference? (vsound = 343m/sec)

A) 2110Hz

B) 2350Hz

C) 2420Hz

D) 2710Hz

2.4m

15m

Phase Angle

Shift written in terms of

“phase angle”

y1(x,t) = sin(kx - wt)

f = 2p*(DL/l)

y2(x,t) = sin(kx - wt + f)

Phase Angle

Constructive

Shifted by n*2p

just some integer (0, 1, 2, 3, 4……)

Destructive

Difference in phase (n+1/2)*2p

Sometimes use “m” instead of “n”

Sometimes f is in degrees f = 360o*Dx/l

Intensity


Recall

Power = Energy/Time

Intensity = Power/Area

= Energy/Time*Area

α Amplitude2*w2

Related to how loud it sounds

Example 24.3 (Intensity)


A ringing bells put out 5 Joules of

sound energy every second. The

sound goes uniformly in all

directions.

What is the intensity of this sound

2m away from the bell?

What is the intensity 4m away?

Intensity Level


Doubling intensity does not double the “loudness”

of the sound to you.

Human “loudness scale” approximated by

Intensity Level, b

b = 10db log (I/Io)

Recall:

• 10n = y n = log(y)

• log(1) = 0

• log(10) = 1

• log(100) = 2

Io = 10-12 Watt/m2

lowest threshold of hearing

Small changes in value of Intensity Level

BIG changes in power output

Example 24.4 (Intensity Level)


A ringing bells put out 5 Joules of

sound energy every second. The

sound goes uniformly in all

directions.

What is the intensity level of this

sound 2m away from the bell?

What is the intensity level 4m

away?

Intensity Level


Two physics students shout at a poor physics

instructor each with an intensity level of 60dB.

What is the intensity level of their combined

voices?

A. Greater than 120dB

B. 120dB

C. Less than 120dB, but greater than 60dB

D. 60dB

E. Less than 60dB

Intensity Level


A quiet radio has an intensity level of about 40 dB.

Busy street traffic has a level of about 70 dB.

How much greater is the intensity of the street

traffic compared to the radio?

A. about 7/4 greater

B. about 7/3 greater

C. about 70/4 greater

D. about 100 times greater

E. about 1000 times greater

Intensity Level


where and

Resonance Patterns/Harmonics


Recall resonance for string instrument

Note the

frequency

pattern:

f = n*v/2L

n=1,2,3,4,5…

These happen

because the

wave reflects from

a node. (We can’t

change the

position.)

Sound is longitudinal wave - media oscillates back and forth in the

direction of travel of the wave

Sound Waves


direction of travel

direction of oscillations

longitudinal displacement (seen another way –> pressure)

x

Open Ended Wind Instruments


Sound wave will reflect off either

end of a enclosed pipe…

even if

it’s open.

Air is completely free to move at

open end. motion anti-node

l/4

Open Ended Wind Instruments


l/4 These happen because

the wave reflects from a

anti-node. (We can’t

change the pressure.)

DEMO

http://www.acs.psu.edu/drussell/Demos/reflect/reflect.html


diagram

from week’s

lab.

where and


Note the

frequency

pattern:

f = n*v/4L

n=1,3,5,7,9…

Even

harmonics

are missing

f = (n-1/2)*v/8L

l = 8L/(n-1/2)

n=1,2,3,4,5…

Example 24.4 Resonance in Tube


You have a tube that is 15cm long

with one end up and one end closed

(like in lab). What is the fundamental

frequency?

That is, what tuning fork you could

hold over the open end so that it

would resonant at it fundamental

frequency?

Question


You have a tube that is 15cm long with one

end up and one end closed (like in lab). We

just found fundamental frequency was

572Hz.

What is the frequency for the first overtone?

A) 858Hz

B) 1144Hz

C) 1716Hz

D) 2288Hz

E) 2860Hz

Question - Resonance in Tube


You have a tube that is 15cm long with one

end up and one end closed (like in lab). We

just found fundamental frequency was

572Hz.

What if both ends were open? What would

be the fundamental frequency now?

A) 143Hz

B) 286HZ

C) 572Hz

D) 1144Hz

E) 2288HZ


Doppler Effect

Image a speaker put out a uniform tone in all

directions.

Distance between waves

peaks is v*T = l

Distance between

waves peaks is

v*T – vE*T = l’

Now image

the speaker

moves

forward as it

puts out

sound


Doppler Effect (moving observer)

What if the observer moves?

= fE (1+vR/fsl)

Observer now “runs into” more

waves per second than before.

Hear higher frequency.

fR = fE +vR/l

= fE (1+vR/vS)

fR = fE(1 +/- vR/vsound)

(1 -/+ vE/vsound)

Combine the two

equations


Example 24.3 (police car)

A police car is moving to the left at 34m/sec while its

siren is emitting a 600Hz tone.

What tone would you hear if you were parked along

side the road?

What tone would you hear if the police car were parked

and you were moving towards the police car at

34m/sec?

What if you are both moving at 34m/sec?

Question


For reasons that are not clear, Jane and Frank are

standing in the middle of the road as a Naperville

police car approaches with its siren on. The siren

emits a 9000Hz tone. Jane is 20 meters in front of

the car and Frank is 40 in front of the car. Who hears

a higher tone from the siren?

A) Frank

B) Jane

C) The both hear the same frequency.

JaneFrank

Question


For reasons that are still not clear, Jane and Frank

are still standing in the middle of the road as a

Naperville police car comes along with its siren on.

But now the car has pasted Jane so she is 10 meters

behind the car and Frank is 10 meters in front of the

car. Who hears a higher tone from the siren?

A) Frank

B) Jane

C) The both hear the same frequency.

JaneFrank

But something odd happens when added two sound waves with slightly different frequencies. Let’s do the math….

where

Beats


Y(x,t)total = A*sin(k1x-w1t) + A*sin(k2x-w2t)

Second, recall:

sin(a) + sin(b) = 2sin((a+b)/2)*cos((a-b)/2)

We know to find the resultant of two different waves at the same spot, you just add the two wave functions……

First, since we’re only going to look at one point in space, so the kx terms are constant…. We can ignore them.

So we’d wind up with something that looked like…….

where and

cos(wLt) sin(wHt)

Beats

( )212

1www -L

( )21 fffBeat -

( ) ( )ttAtAtA LH wwww cossin2)sin()sin( 21 +


( )212

1www +H

physics 2111 unit 24 - college of dupagesound is longitudinal wave - media oscillates back and forth...

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