# 8.1 Applications  (Page 2/3)

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## Interesting fact

Ultrasound generator/speaker systems are sold with claims that they frighten away rodents and insects, but there is no scientific evidence that the devices work; controlled tests have shown that rodents quickly learn that the speakers are harmless.

In echo-sounding the reflections from ultrasound pulses that are bounced off objects (for example the bottom of the sea, fish etc.) are picked up. The reflections are timed and since their speed is known, the distance to the object can be found. This information can be built into a picture of the object that reflects the ultrasound pulses.

## Sonar

Ships on the ocean make use of the reflecting properties of sound waves to determine the depth of the ocean. A sound wave is transmitted and bounces off the seabed. Because the speed of sound is known and the time lapse between sending and receiving the sound can be measured, the distance from the ship to the bottom of the ocean can be determined, This is called sonar, which stands from So und N avigation A nd R anging.

## Echolocation

Animals like dolphins and bats make use of sounds waves to find their way. Just like ships on the ocean, bats use sonar to navigate. Ultrasound waves that are sent out are reflected off the objects around the animal. Bats, or dolphins, then use the reflected sounds to form a “picture” of their surroundings. This is called echolocation.

A ship sends a signal to the bottom of the ocean to determine the depth of the ocean. The speed of sound in sea water is $1450\phantom{\rule{2pt}{0ex}}\mathrm{m}.{\mathrm{s}}^{-1}$ . If the signal is received 1,5 seconds later, how deep is the ocean at that point?

1. $\begin{array}{ccc}\hfill s& =& 1450\phantom{\rule{4pt}{0ex}}\mathrm{m}.{\mathrm{s}}^{-1}\hfill \\ \hfill t& =& 1,5\phantom{\rule{4pt}{0ex}}\mathrm{s}\phantom{\rule{4pt}{0ex}}\mathrm{there}\phantom{\rule{4pt}{0ex}}\mathrm{and}\phantom{\rule{4pt}{0ex}}\mathrm{back}\hfill \\ \hfill \therefore t& =& 0,75\phantom{\rule{4pt}{0ex}}\mathrm{s}\phantom{\rule{4pt}{0ex}}\mathrm{one}\phantom{\rule{4pt}{0ex}}\mathrm{way}\hfill \\ \hfill D& =& ?\hfill \end{array}$
2. $\begin{array}{ccc}\hfill \mathrm{Distance}& =& \mathrm{speed}×\mathrm{time}\hfill \\ \hfill D& =& s×t\hfill \\ & =& 1450\phantom{\rule{2pt}{0ex}}\mathrm{m}.{\mathrm{s}}^{-1}×0,75s\hfill \\ & =& 1087,5\phantom{\rule{4pt}{0ex}}\mathrm{m}\hfill \end{array}$

## Intensity of sound (not included in caps - advanced)

This section is more advanced than required and is best revisited for interest only when you are comfortable with concepts like power and logarithms.

Intensity is one indicator of amplitude. Intensity is the energy transmitted over a unit of area each second.

## Intensity

Intensity is defined as:

$\mathrm{Intensity}=\frac{\mathrm{energy}}{\mathrm{time}×\mathrm{area}}=\frac{\mathrm{power}}{\mathrm{area}}$

By the definition of intensity, we can see that the units of intensity are

$\frac{\mathrm{Joules}}{\mathrm{s}·{\mathrm{m}}^{2}}=\frac{\mathrm{Watts}}{{\mathrm{m}}^{2}}$

The unit of intensity is the decibel (symbol: dB). This reduces to an SI equivalent of $\mathrm{W}·{\mathrm{m}}^{-2}$ .

The average threshold of hearing is ${10}^{-12}\phantom{\rule{3.33333pt}{0ex}}\mathrm{W}·{\mathrm{m}}^{-2}$ . Below this intensity, the sound is too soft for the ear to hear. The threshold of pain is $1.0\phantom{\rule{3.33333pt}{0ex}}\mathrm{W}·{\mathrm{m}}^{-2}$ . Above this intensity a sound is so loud it becomes uncomfortable for the ear.

Notice that there is a factor of ${10}^{12}$ between the thresholds of hearing and pain. This is one reason we define the decibel (dB) scale.

In this way we can compress the whole hearing intensity scale into a range from 0 dB to 120 dB.

 Source Intensity (dB) Times greater than hearing threshold Rocket Launch 180 ${10}^{18}$ Jet Plane 140 ${10}^{14}$ Threshold of Pain 120 ${10}^{12}$ Rock Band 110 ${10}^{11}$ Subway Train 90 ${10}^{9}$ Factory 80 ${10}^{8}$ City Traffic 70 ${10}^{7}$ Normal Conversation 60 ${10}^{6}$ Library 40 ${10}^{4}$ Whisper 20 ${10}^{2}$ Threshold of hearing 0 0

explain and give four Example hyperbolic function
The denominator of a certain fraction is 9 more than the numerator. If 6 is added to both terms of the fraction, the value of the fraction becomes 2/3. Find the original fraction. 2. The sum of the least and greatest of 3 consecutive integers is 60. What are the valu
1. x + 6 2 -------------- = _ x + 9 + 6 3 x + 6 3 ----------- x -- (cross multiply) x + 15 2 3(x + 6) = 2(x + 15) 3x + 18 = 2x + 30 (-2x from both) x + 18 = 30 (-18 from both) x = 12 Test: 12 + 6 18 2 -------------- = --- = --- 12 + 9 + 6 27 3
Pawel
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x-2y+3z=-3 2x-y+z=7 -x+3y-z=6
can you teacch how to solve that🙏
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Solve for the first variable in one of the equations, then substitute the result into the other equation. Point For: (6111,4111,−411)(6111,4111,-411) Equation Form: x=6111,y=4111,z=−411x=6111,y=4111,z=-411
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x=61/11 y=41/11 z=−4/11 x=61/11 y=41/11 z=-4/11
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