physics 6b
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Physics 6B. Decibels and Doppler Effect. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB. Sound Intensity and Decibel Level. Formulas: Basic rule of thumb: for each factor of 10 change in intensity, add or subtract 10 dB. Prepared by Vince Zaccone - PowerPoint PPT PresentationTRANSCRIPT
Physics 6B
Decibels and Doppler Effect
Prepared by Vince Zaccone
For Campus Learning Assistance Services at UCSB
Sound Intensity and Decibel Level
• Formulas:
Basic rule of thumb:for each factor of 10 change in intensity, add or subtract 10 dB
2mW12
00
2
10I;II
log10
R
1I
AreaPower
I
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:
Prepared by Vince Zaccone
For Campus Learning Assistance Services at UCSB
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)
similar to 12.70 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 by the mother?
Prepared by Vince Zaccone
For Campus Learning Assistance Services at UCSB
similar to 12.70 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 by the 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
similar to 12.70 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 by the 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 when we compare the father and mother.Since sound intensity depends on 1/r2, the mother’s intensity is 1/100 times the father’s intensity.
Prepared by Vince Zaccone
For Campus Learning Assistance Services at UCSB
similar to 12.70 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 by the 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 when we compare the father and mother.Since sound intensity depends on 1/r2, the mother’s intensity is 1/100 times the father’s intensity.
This is 2 factors of 10.
Prepared by Vince Zaccone
For Campus Learning Assistance Services at UCSB
similar to 12.70 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 by the 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 when we compare the father and mother.Since sound intensity depends on 1/r2, the mother’s intensity is 1/100 times the father’s intensity.
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
similar to 12.70 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 by the 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 when we compare the father and mother.Since sound intensity depends on 1/r2, the mother’s intensity is 1/100 times the father’s intensity.
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 levels 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
similar to 12.70 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 by the 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 when we compare the father and mother.Since sound intensity depends on 1/r2, the mother’s intensity is 1/100 times the father’s intensity.
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 levels 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
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
Doppler Effect
Basic 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 seem to have lower frequencies.
Prepared by Vince Zaccone
For Campus Learning Assistance Services at UCSB
Doppler Effect
Basic 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 seem to have lower frequencies.
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.
Prepared by Vince Zaccone
For Campus Learning Assistance Services at UCSB
170 m/s
340 m/s
Doppler Effect
Basic 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 seem to have lower frequencies.
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, so motion toward = upward shift in frequency
Prepared by Vince Zaccone
For Campus Learning Assistance Services at UCSB
170 m/s
340 m/s
Doppler Effect
Basic 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 seem to have lower frequencies.
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, so 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, so motion away = downward shift in frequency
Prepared by Vince Zaccone
For Campus Learning Assistance Services at UCSB
170 m/s
340 m/s
Doppler Effect
Basic 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 seem to have lower frequencies.
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, so 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, so 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!
Prepared by Vince Zaccone
For Campus Learning Assistance Services at UCSB
170 m/s
340 m/s
Prepared by Vince Zaccone
For Campus Learning Assistance Services at UCSB
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)
Here is a basic type of conceptual 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
Here is a basic type of conceptual 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.
Case 1: The ice cream truck is approaching your house at 10 m/s.What is the frequency of the sound you hear?a)971 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
Here is a basic type of conceptual 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.
Case 1: The ice cream truck is approaching your house at 10 m/s.What is the frequency of the sound you hear?a)971 Hzb)1000 Hzc)1030 Hzd)who cares – give me the ice cream already!!
The correct answer is c)The truck is moving toward you, so there is an upward shift in frequency.answer d) is also correct
v=10m/s
Prepared by Vince Zaccone
For Campus Learning Assistance Services at UCSB
Here is a basic type of conceptual 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.
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)971 Hzb)1000 Hzc)1030 Hzd)you can’t hear anything over the sound of your sobbing – you missed the ice cream truck!!
v=10m/s
Prepared by Vince Zaccone
For Campus Learning Assistance Services at UCSB
Here is a basic type of conceptual 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.
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)971 Hzb)1000 Hzc)1030 Hzd)you can’t hear anything over the sound of your sobbing – you missed the ice cream truck!!
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
Here is a basic type of conceptual 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.
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 is the frequency of the sound she hears?a) 986 Hzb) 1000 Hzc) 1014 Hzd) you can’t hear anything because you are screaming for ice cream!
v=10m/sv=15m/s
Prepared by Vince Zaccone
For Campus Learning Assistance Services at UCSB
Here is a basic type of conceptual 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 an upward shift in the frequency.answer d) may also be correct – it depends upon the availability of your favorite flavor.
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 is the frequency of the sound she hears?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
Here is a basic type of conceptual 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.
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 is the frequency of the sound she hears?a) 986 Hzb) 1000 Hzc) 1014 Hzd) you can’t hear anything because you are screaming for ice cream!
v=10m/sv=15m/s
Prepared by Vince Zaccone
For Campus Learning Assistance Services at UCSB