Physics 6B

Decibels and Doppler Effect

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For Campus Learning Assistance Services at UCSB

Sound Intensity and Decibel Level

• Formulas:Intensity increases as the square of the wave

Amplitude.

Basic rule of thumb:for each factor of 10 change in intensity, add or subtract 10 dB

2

120

0

2

2

10;log10

1

mWI

II

RI

AreaPower

I

AI

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

Sound Intensity and Decibel Level

• How to calculate decibels from intensity:Suppose a sound has intensity I=10-3 W/m2.To find the Intensity Level (in dB) we can use the definition:

• How to calculate intensity from decibels:Suppose a sound has a sound level of 73 dB.To Find the intensity (in W/m2) we use the definition again:

dB90)10log(1010

10log10

10I;II

log10

9

mW12

mW3

mW12

00

2

2

2

22

22

22

2

mW5

mW53.0

mW12

73.0

mW12

3.7

mW12

mW12

mW12

00

1021010I

10I

101010

I10

)10

Ilog(3.7)

10I

log(10dB73

10I;II

log10

Another rule of thumb we get from this is that a 3dB change means a factor of 2 change in intensity.(73dB is twice the intensity of 70dB)

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

Example - A baby’s mouth is 30.0 cm from her father’s ear and 3.0m from her mother’s ear. What is the difference of the sound intensity levels (in dB) heard by the father and mother?

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

Example - A baby’s mouth is 30.0 cm from her father’s ear and 3.0m from her mother’s ear. What is the difference of the sound intensity levels (in dB) heard by the father and mother?

The first step is to find the ratio of the distances. Just divide them to find that the mother is 10 times farther away.Don’t forget to look at the units – 3.0m is 300cm.

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

Example - A baby’s mouth is 30.0 cm from her father’s ear and 3.0m from her mother’s ear. What is the difference of the sound intensity levels (in dB) heard by the father and mother?

The first step is to find the ratio of the distances. Just divide them to find that the mother is 10 times farther away.Don’t forget to look at the units – 3.0m is 300cm.

Now we can use this to find out what happens to the intensity.Since sound intensity depends on 1/r2, the mother’s intensity is 1/100 times the father’s.

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

Example - A baby’s mouth is 30.0 cm from her father’s ear and 3.0m from her mother’s ear. What is the difference of the sound intensity levels (in dB) heard by the father and mother?

The first step is to find the ratio of the distances. Just divide them to find that the mother is 10 times farther away.Don’t forget to look at the units – 3.0m is 300cm.

Now we can use this to find out what happens to the intensity.Since sound intensity depends on 1/r2, the mother’s intensity is 1/100 times the father’s.

This is 2 factors of 10.

For each factor of 10 change in intensity, you change the sound level by 10 decibels.

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

Example - A baby’s mouth is 30.0 cm from her father’s ear and 3.0m from her mother’s ear. What is the difference of the sound intensity levels (in dB) heard by the father and mother?

The first step is to find the ratio of the distances. Just divide them to find that the mother is 10 times farther away.Don’t forget to look at the units – 3.0m is 300cm.

Now we can use this to find out what happens to the intensity.Since sound intensity depends on 1/r2, the mother’s intensity is 1/100 times the father’s.

This is 2 factors of 10.

For each factor of 10 change in intensity, you change the sound level by 10 decibels.

So the difference in sound intensity level is 20 dB.For example, if the father hears an 80 dB sound, the mother will hear 60 dB.

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

Example - A baby’s mouth is 30.0 cm from her father’s ear and 3.0m from her mother’s ear. What is the difference of the sound intensity levels (in dB) heard by the father and mother?

The first step is to find the ratio of the distances. Just divide them to find that the mother is 10 times farther away.Don’t forget to look at the units – 3.0m is 300cm.

Now we can use this to find out what happens to the intensity.Since sound intensity depends on 1/r2, the mother’s intensity is 1/100 times the father’s.

This is 2 factors of 10.

For each factor of 10 change in intensity, you change the sound level by 10 decibels.

So the difference in sound intensity level is 20 dB.For example, if the father hears an 80 dB sound, the mother will hear 60 dB.

The more math-y version of the solution is below. It’s best if you can do it both ways.

r1=30cm=0.3m; r2=3mSince Intensity is proportional to 1/r2, we can write: 222221 m9

C)m3(

CI;

m09.0C

)m3.0(C

I

Now we can write the equations for the decibel levels:

dB20)100log(10)II

log(10)II

log()II

log(10

)II

log(10

)II

log(10

2

1

0

2

0

121

0

22

0

11

We need the difference, so subtract them (and simplify using log rules)

100II

m9

Cm09.0

C

II

2

1

2

2

2

1

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

Doppler EffectBasic Idea: Things sound different when objects are moving relative to each other.

If objects are moving toward each other, sounds seem to have higher frequencies.If objects are moving away from each other, sounds have lower frequencies.

If the source of the sound is moving, the wavelength will change as well.

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

Doppler EffectBasic Idea: Things sound different when objects are moving relative to each other.

If objects are moving toward each other, sounds seem to have higher frequencies.If objects are moving away from each other, sounds have lower frequencies.

If the source of the sound is moving, the wavelength will change as well.

Here is a quick explanation:If you are standing on either side of a stationary car, you will hear the same sound because the sound waves hit you at the same frequency.

However, if you are near a moving car, the frequencies are different depending on where you stand.

In front of the car, the waves are bunched up, so the frequency is increased. The car is moving toward you.motion toward = upward shift in frequency

Behind the car, the waves are spread out, so the frequency is decreased. The car is moving away from you.motion away = downward shift in frequency

170 m/s

340 m/s

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

Doppler EffectBasic Idea: Things sound different when objects are moving relative to each other.

If objects are moving toward each other, sounds seem to have higher frequencies.If objects are moving away from each other, sounds have lower frequencies.

If the source of the sound is moving, the wavelength will change as well.

Here is a quick explanation:If you are standing on either side of a stationary car, you will hear the same sound because the sound waves hit you at the same frequency.

However, if you are near a moving car, the frequencies are different depending on where you stand.

In front of the car, the waves are bunched up, so the frequency is increased. The car is moving toward you.motion toward = upward shift in frequency

Behind the car, the waves are spread out, so the frequency is decreased. The car is moving away from you.motion away = downward shift in frequency

Note that the bottom car is moving at the speed of sound (are we sure it’s not an airplane??), so the waves in front are so bunched up that they hit you all at once when the car drives by – that’s a sonic boom!

170 m/s

340 m/s

Formula for Doppler Shift

S

LSL vv

vvff

In this formula v is the speed of the waves.

L is for Listener, and S is for Source.

Set up your coordinate system so that positive is away from the listener and toward the source.

OR

Choose the plus/minus signs based on the situation:

•If the motion is toward, the fraction has to come out larger than 1 (to get an upward shift in frequency)

•If the motion is away, the fraction has to come out less than 1 (to get a downward shift in frequency) Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

Doppler Effect

Example: On a hot afternoon you hear an ice cream truck down the street. The truck’s music box is broken, so it just emits a continuous tone at exactly 1000 Hz.

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

Case 1: The ice cream truck is approaching your house at 10 m/s.What is the frequency of the sound you hear?a)972 Hzb)1000 Hzc)1030 Hzd)who cares – give me the ice cream already!!

v=10m/s

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

Example: On a hot afternoon you hear an ice cream truck down the street. The truck’s music box is broken, so it just emits a continuous tone at exactly 1000 Hz.

The correct answer is c)The truck is moving toward you, so there is an upward shift in frequency.answer d) is also correct

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

Example: On a hot afternoon you hear an ice cream truck down the street. The truck’s music box is broken, so it just emits a continuous tone at exactly 1000 Hz.

v=10m/s

Case 1: The ice cream truck is approaching your house at 10 m/s.What is the frequency of the sound you hear?a)972 Hzb)1000 Hzc)1030 Hzd)who cares – give me the ice cream already!!

Here is the calculation using our Doppler shift formula:

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

Example: On a hot afternoon you hear an ice cream truck down the street. The truck’s music box is broken, so it just emits a continuous tone at exactly 1000 Hz.

v=10m/s

Case 1: The ice cream truck is approaching your house at 10 m/s.What is the frequency of the sound you hear?a)972 Hzb)1000 Hzc)1030 Hzd)who cares – give me the ice cream already!!

S

LSL vv

vvff

HzHzfsm

sm

sm

L 103010343

03431000

Positive Direction

Negative Sign on bottom makes the fraction bigger than 1

Case 2: The ice cream truck has passed by your house and is driving away at 10 m/s.What is the frequency of the sound you hear?a)972 Hzb)1000 Hzc)1030 Hzd)you can’t hear anything over the sound of your sobbing – you missed the ice cream truck!!

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

Example: On a hot afternoon you hear an ice cream truck down the street. The truck’s music box is broken, so it just emits a continuous tone at exactly 1000 Hz.

v=10m/s

The correct answer is a)The truck is moving away from you, so there is a downward shift in frequency.answer d) is not correct – you can still catch the truck. hurry! run!!

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

Example: On a hot afternoon you hear an ice cream truck down the street. The truck’s music box is broken, so it just emits a continuous tone at exactly 1000 Hz.

v=10m/s

Case 2: The ice cream truck has passed by your house and is driving away at 10 m/s.What is the frequency of the sound you hear?a)972 Hzb)1000 Hzc)1030 Hzd)you can’t hear anything over the sound of your sobbing – you missed the ice cream truck!!

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

Example: On a hot afternoon you hear an ice cream truck down the street. The truck’s music box is broken, so it just emits a continuous tone at exactly 1000 Hz.

v=10m/s

Case 2: The ice cream truck has passed by your house and is driving away at 10 m/s.What is the frequency of the sound you hear?a)972 Hzb)1000 Hzc)1030 Hzd)you can’t hear anything over the sound of your sobbing – you missed the ice cream truck!!

Here is the calculation using our Doppler shift formula:S

LSL vv

vvff

HzHzfsm

sm

sm

L 97210343

03431000

Positive Direction

Positive Sign on bottom makes the fraction smaller than 1

Case 3: The ice cream truck has passed by your house and is driving away at 10 m/s. Your mom chases the truck at her top speed of 15 m/s. What frequency sound does she hear?a) 986 Hzb) 1000 Hzc) 1014 Hzd) you can’t hear anything because you are screaming for ice cream!

v=15m/s

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

Example: On a hot afternoon you hear an ice cream truck down the street. The truck’s music box is broken, so it just emits a continuous tone at exactly 1000 Hz.

v=10m/s

The correct answer is c) – the truck is moving away from you, but you are chasing it. Since your speed is greater than the truck, your relative velocity is toward, so there is a net upward shift in the frequency.answer d) may also be correct – it depends upon the availability of your favorite flavor.

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

Example: On a hot afternoon you hear an ice cream truck down the street. The truck’s music box is broken, so it just emits a continuous tone at exactly 1000 Hz.

v=10m/s

v=15m/s

Case 3: The ice cream truck has passed by your house and is driving away at 10 m/s. Your mom chases the truck at her top speed of 15 m/s. What frequency sound does she hear?a) 986 Hzb) 1000 Hzc) 1014 Hzd) you can’t hear anything because you are screaming for ice cream!

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

Example: On a hot afternoon you hear an ice cream truck down the street. The truck’s music box is broken, so it just emits a continuous tone at exactly 1000 Hz.

v=10m/s

v=15m/s

Case 3: The ice cream truck has passed by your house and is driving away at 10 m/s. Your mom chases the truck at her top speed of 15 m/s. What frequency sound does she hear?a) 986 Hzb) 1000 Hzc) 1014 Hzd) you can’t hear anything because you are screaming for ice cream!

Here is the calculation using our Doppler shift formula:S

LSL vv

vvff

HzHzfsm

sm

sm

sm

L 101410343

153431000

Positive Direction

Positive Sign on bottom makes the fraction smaller than 1

Positive Sign on top makes the fraction bigger than 1