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course Phy 202
3/23 10 This is not complete, but I need some guidance.
110307 Physics
For 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
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100=10^2
10000=10^4
.0001=10^ -4
10 000 000 000 000 =10^13
10^5/10^14=10^-9
100/10^7=10^-5
@& All of your statement are correct, but you haven't given the logs, which are respectively
2
4
-4
13
-9
5
The log is the power to which you raise 10.*@
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`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?
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The slopes are the same
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`q003. Using your graphs from before, estimate the following:
• log(3)
• log(5)
• log(300)
• log(500)
• log(2 000 000)
****
Respectively
.5
.7
2.3
2.8
6.1
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`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)
****
Respectively
8.5
10
-4.3
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`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?
****
The pain threshold is 12 times more intense
log is 12= 1.08
@& The ratio of the intensitives is 1 / 10^-12 = 10^12.
So the pain threshold is 10^12 times as intense as the hearing threshold.
12 is the log of this ratio, not the ratio itself.
1.08 is the log of 12, but 12 is the log of the ratio. You wouldn't calculate a log of a log.*@
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`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
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respectively
8 times
4 times
How do you determine based on the different numbers?
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`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
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I’m confused. Log of 5 is ~.7. So is the intensity .7 times greater than the hearing threshold?
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`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
****
@& 8 and 4 are the logs of the ratios.
The ratios are 10^8 and 10^4, so the first is 10^8 times as intense as the eharing threshold, the second 10^4 times as intense.
It's not correct to say that the first is 8 times as great as anything; 8 is the log of how many times greater it is.
For .03 watts / m^2, the ratio to hearing threshold is .03 / 10^-12 = 3 * 10^10. To estimate the log of 3 * 10^10, you would relabel your graph from the first problem. 3 * 10^10 is between 10^10 and 10^11, so your horizontal axis points would be 10^9, 10^10 and 10^11.
Your vertical axis points would be the logs of these numbers, which are 9, 10 and 11.
3 * 10^10 is closer to 10^10 than to 10^11, but the curvature of the graph will put the log about halfway between 10 and 11, around 10.5.
Similarly you relabel again for the last question. 5 * 10^-7 is between 10^-7 and 10^-6, so x axis points would be 10^-8, 10^-7 and 10^-6. y axis labels would be -8, -7 and -6. The log would be between -7 and -8.*@
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`q009. What is the intensity of a sound with each of the following decibel levels?
• 80 dB
• 25 dB
• 53 dB
• 110 dB
@& 80 dB means that 10 db * log(intensity ratio) = 80 dB, so log(intensity ratio) = 80 / 10 = 8.
If the log of a number is 8, then the number is 10^8. So the intensity ratio is 10^8.
The intensity ratio is the ratio of the sound's intensity to hearing threshold intensity.
Thus
I / (10^-12 watts / m^2) = 10^8
and
I = 10^8 * 10^-12 watts / m^2 = 10^-4 watts / m^s.*@
@& See if you can use this reasoning to figure out the other intensity ratios.*@
@& *@
`q010. What is the ratio of the intensities of two sounds whose decibel levels differ by 33 dB?
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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?
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`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?
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