#$&*
course Phy 242
March 24 around 4:30pm.
110307`q001. The log of a number is the power to which you need to raise 10 to get that number. What are the logs of the following numbers?
100
10000
.0001
10 000 000 000 000
10^5 / 10^14
100 / 10^7
****
2
4
-4
13
-9
-5
#$&*
`q002. Quickly sketch the following graphs
log(x) vs. x from x = 1 to x = 100
log(x) vs. x from x = 10 to x = 1 000
log(x) vs. x from x = 100 000 to 10 000 000
log(x) from x = 0.1 to x = 10.
What do your graphs have in common?
****
They all are the same curve, obviously, because its log(x). But when you graph these, the steepness changes because the intervals are different. For example, 0.1 to 10 is going to be a steeper curve than the others, because the others are going to eventually look like a straight horizontal line.
@& Identical curves can simply be relabeled for every new situation. The shape of the curve doesn't need to change.
However you are right about the actual slope changing. The rises wouldn't change, but since the x scale is changing by multples of 10, the slopes represented by the graphs would change with each relabeling.*@
#$&*
`q003. Using your graphs from before, estimate the following:
log(3)
log(5)
log(300)
log(500)
log(2 000 000)
****
A little over a half
1
@& log(10) is 1. log(5) is more like .7.*@
3
@& log(1000) = 3.
log(100) = 2.
The shape of the graph will show you roughly what the log of 300 should be.*@
3.5
@& The graph has more concavity than you're giving it credit for. log(500) is closer to 3 than to 2.*@
6
@& log(1 000 000) is 6.
log(2 000 000) is more than 6. It's between 6 and 7. Take the shape of the curve into account.*@
I estimated all these, so Im sure theyre not perfect.
#$&*
`q004. Relabel one or more of your graphs to estimate each of the following:
log(300 000 000)
log(5 000 000 000)
log(.00003)
****
10
11
-5
@& None of these numbers are powers of 10, so none will have integer values for their logs.
Can you describe how you're relabeling the graphs?*@
#$&*
`q005. The hearing threshold is defined to be 10^-12 watts / m^2. We can stand sounds up to intensity 1 watt / m^2 without pain. 1 watt / m^2 is called the pain threshold.
How many times more intense than the hearing threshold is the pain threshold?
What is the log of this ratio?
****
1 * 10^12 more intense
12
#$&*
`q006. Based on your graph(s), what is the log of the ratio of each of the following intensities to the hearing threshold?
.0001 watts / m^2
10^-8 watts / m^2
.03 watts / m^2
5 * 10^-7 watts / m^2
****
-5
-8
-1
-7
Using my best estimation.
@& You have to start by finding the ratio of each intensity to hearing threshold intensity. The first is 10^8 times hearing threshold, so the log of the ratio would be 8,*@
#$&*
`q007. If the log of the ratio of intensity to hearing threshold intensity is the given number, then what is the intensity?
5
9
3.5
****
100 000
1 000 000 000
3100
@& For example, your first number 100 000 is the ratio of intensities.
Hearing threshold intensity is 10^-12 watts.
What therefore is the intensity of the sound?*@
#$&*
`q008. The decibel level of a sound is 10 times the log of the ratio of its intensity to the hearing threshold intensity. What is the decibel level of each of the following, which you have seen in a previous question:
.0001 watts / m^2
10^-8 watts / m^2
.03 watts / m^2
5 * 10^-7 watts / m^2
****
1 DB is 10*log(ratio)
-40
-80
-15
-63
@& You're finding 10 times the log of the number, not 10 times the log of the ratio of that number to hearing threshold.*@
#$&*
`q009. What is the intensity of a sound with each of the following decibel levels?
80 dB
25 dB
53 dB
110 dB
****
1 * 10^(-4)
3.2 * 10^(-10)
2 * 10^(-7)
0.1
@& These are correct.*@
#$&*
`q010. What is the ratio of the intensities of two sounds whose decibel levels differ by 33 dB?
****
#$&*
University Physics:
`q011. If the waveforms y_1 = A cos(omega * t) and y_2 = A cos( (omega + `dOmega) t are mixed, what is the equation of the combined wave function, in terms of sines and cosines of omega * t and `dOmega * t?
What is the maximum amplitude of the resulting beats?
****
Y1 = A sin (omega*t - kx)
Y2 = A sin (omega*t - k(x-a sin theta))
@& The beat occurs every time the waves are in phase.
The two waves have the same amplitude, so when they're in phase the amplitude will be double the amplitude of each.*@
#$&*
`q012. A speaker suspended by its power cord oscillates back and forth with an amplitude of 10 cm and a frequency of 40 cycles / minute. It emits sound at 1000 Hz. A microphone is mounted in front of the speaker, and another behind it, so that when the speaker moving toward one microphone it is moving away from the other. Both speakers are at some distance from the speaker.
The sound collected by the microphones is mixed into a single sound.
What is the maximum frequency of the resulting beats?
****
#$&*
"
Self-critique (if necessary):
------------------------------------------------
Self-critique rating:
@& You're within striking distance. Shouldn't be difficult to modify and get just about everything right.
`gr99
*@
#$&*
course Phy 242
March 24 around 4:30pm.
110307`q001. The log of a number is the power to which you need to raise 10 to get that number. What are the logs of the following numbers?
100
10000
.0001
10 000 000 000 000
10^5 / 10^14
100 / 10^7
****
2
4
-4
13
-9
-5
#$&*
`q002. Quickly sketch the following graphs
log(x) vs. x from x = 1 to x = 100
log(x) vs. x from x = 10 to x = 1 000
log(x) vs. x from x = 100 000 to 10 000 000
log(x) from x = 0.1 to x = 10.
What do your graphs have in common?
****
They all are the same curve, obviously, because its log(x). But when you graph these, the steepness changes because the intervals are different. For example, 0.1 to 10 is going to be a steeper curve than the others, because the others are going to eventually look like a straight horizontal line.
@& Identical curves can simply be relabeled for every new situation. The shape of the curve doesn't need to change.
However you are right about the actual slope changing. The rises wouldn't change, but since the x scale is changing by multples of 10, the slopes represented by the graphs would change with each relabeling.*@
#$&*
`q003. Using your graphs from before, estimate the following:
log(3)
log(5)
log(300)
log(500)
log(2 000 000)
****
A little over a half
1
@& log(10) is 1. log(5) is more like .7.*@
3
@& log(1000) = 3.
log(100) = 2.
The shape of the graph will show you roughly what the log of 300 should be.*@
3.5
@& The graph has more concavity than you're giving it credit for. log(500) is closer to 3 than to 2.*@
6
@& log(1 000 000) is 6.
log(2 000 000) is more than 6. It's between 6 and 7. Take the shape of the curve into account.*@
I estimated all these, so Im sure theyre not perfect.
#$&*
`q004. Relabel one or more of your graphs to estimate each of the following:
log(300 000 000)
log(5 000 000 000)
log(.00003)
****
10
11
-5
@& None of these numbers are powers of 10, so none will have integer values for their logs.
Can you describe how you're relabeling the graphs?*@
#$&*
`q005. The hearing threshold is defined to be 10^-12 watts / m^2. We can stand sounds up to intensity 1 watt / m^2 without pain. 1 watt / m^2 is called the pain threshold.
How many times more intense than the hearing threshold is the pain threshold?
What is the log of this ratio?
****
1 * 10^12 more intense
12
#$&*
`q006. Based on your graph(s), what is the log of the ratio of each of the following intensities to the hearing threshold?
.0001 watts / m^2
10^-8 watts / m^2
.03 watts / m^2
5 * 10^-7 watts / m^2
****
-5
-8
-1
-7
Using my best estimation.
@& You have to start by finding the ratio of each intensity to hearing threshold intensity. The first is 10^8 times hearing threshold, so the log of the ratio would be 8,*@
#$&*
`q007. If the log of the ratio of intensity to hearing threshold intensity is the given number, then what is the intensity?
5
9
3.5
****
100 000
1 000 000 000
3100
@& For example, your first number 100 000 is the ratio of intensities.
Hearing threshold intensity is 10^-12 watts.
What therefore is the intensity of the sound?*@
#$&*
`q008. The decibel level of a sound is 10 times the log of the ratio of its intensity to the hearing threshold intensity. What is the decibel level of each of the following, which you have seen in a previous question:
.0001 watts / m^2
10^-8 watts / m^2
.03 watts / m^2
5 * 10^-7 watts / m^2
****
1 DB is 10*log(ratio)
-40
-80
-15
-63
@& You're finding 10 times the log of the number, not 10 times the log of the ratio of that number to hearing threshold.*@
#$&*
`q009. What is the intensity of a sound with each of the following decibel levels?
80 dB
25 dB
53 dB
110 dB
****
1 * 10^(-4)
3.2 * 10^(-10)
2 * 10^(-7)
0.1
@& These are correct.*@
#$&*
`q010. What is the ratio of the intensities of two sounds whose decibel levels differ by 33 dB?
****
#$&*
University Physics:
`q011. If the waveforms y_1 = A cos(omega * t) and y_2 = A cos( (omega + `dOmega) t are mixed, what is the equation of the combined wave function, in terms of sines and cosines of omega * t and `dOmega * t?
What is the maximum amplitude of the resulting beats?
****
Y1 = A sin (omega*t - kx)
Y2 = A sin (omega*t - k(x-a sin theta))
@& The beat occurs every time the waves are in phase.
The two waves have the same amplitude, so when they're in phase the amplitude will be double the amplitude of each.*@
#$&*
`q012. A speaker suspended by its power cord oscillates back and forth with an amplitude of 10 cm and a frequency of 40 cycles / minute. It emits sound at 1000 Hz. A microphone is mounted in front of the speaker, and another behind it, so that when the speaker moving toward one microphone it is moving away from the other. Both speakers are at some distance from the speaker.
The sound collected by the microphones is mixed into a single sound.
What is the maximum frequency of the resulting beats?
****
#$&*
"
Self-critique (if necessary):
------------------------------------------------
Self-critique rating:
@& You're within striking distance. Shouldn't be difficult to modify and get just about everything right.
&#Please see my notes and, unless my notes indicate that revision is optional, submit a copy of this document with revisions and/or questions, and mark your insertions with &&&& (please mark each insertion at the beginning and at the end).
Be sure to include the entire document, including my notes.
If my notes indicate that revision is optional, use your own judgement as to whether a revision will benefit you. &#
*@