Physics
Physics
1st Edition
Walker
ISBN: 9780133256925
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Page 519: Lesson Check

Exercise 53
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The sound is distributed over a larger area as it travels away from the source. Consequently, the intensity is reduced (Intensity is inversely proportional as area). Similarly, as you go closer from the source, more power is subjected to a smaller area. In effect, the sound gets larger.
Result
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Exercise 54
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To compare the loudness ratio an observer will experience when subject to two different alarm clocks, one of which is $20text{ dB}$ louder than the other, we will first remember that:

Our perception of sound is such that doubling the loudness corresponds to increasing the intensity by a factor of 10, which corresponds to an increase of $10text{ dB}$.

Keeping that in mind, a difference of $20text{ dB}$ will produce a doubling effect of the loudness twice. This means that the louder alarm will seem 4 times louder.

Result
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The louder alarm will seem 4 times louder.
Exercise 55
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The intensity of sound coming a from a point source is defined as the power produced divided by its area $4pi r^2$. Since it varies inversely as the square of the distance from the source, the sound intensity decreases by a factor of 4 if the distance is doubled.
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Exercise 56
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When a sound travels, a pressure difference occurs in the areas of compression (high pressure) and rarefaction (low pressure). A pressure does exert force on an object making it capable of doing work, as well as energy transfer. Therefore, regions of compression and rarefaction in sound waves do transfer energy from one place to another.
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Exercise 57
Step 1
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### Theoretical reminder

The amount of energy carried by a sound wave through a given area in a given time is the intensity $I$. It can be calculated via power $P$ and area $A$ as follows:

$$
begin{equation}
I = frac{P}{A}
end{equation}
$$

Step 2
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### Calculation

We know that the intensity of the sound wave is $I = 4.4 cdot 10^{-4} ; frac{text{W}}{text{m}^2}$. And the area through which it passes is $A = 1.8text{ m}^2$

Finding the power of the sound source is done simply, using formula (1) as follows:

$$
begin{align*}
I = frac{P}{A}
end{align*}
$$

Rearranging for $P$ :

$$
begin{align*}
P = I cdot A
end{align*}
$$

Plugging in the values we get:

$$
begin{align*}
P = 4.4 cdot 10^{-4} ; frac{text{W}}{text{m}^2} cdot 1.8text{ m}^2 approx 7.9 cdot 10^{-4}text{ W}
end{align*}
$$

Result
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The power of the sound source is $P = 7.9 cdot 10^{-4}text{ W}$
Exercise 58
Step 1
1 of 3
### Theoretical reminder

The amount of energy carried by a sound wave through a given area in a given time is the intensity $I$. It can be calculated via power $P$ and area $A$ as follows:

$$
begin{align*}
I = frac{P}{A}
end{align*}
$$

For spherical wave expansion the area becomes:

$$
begin{align*}
A = 4 , r^2 , pi
end{align*}
$$

So we get finally:

$$
begin{equation}
I = frac{P}{4 , r^2 , pi}
end{equation}
$$

Where $r$ is the distance from the sound source to the wave front.

Step 2
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### Calculation

We know the power of the sound source is $P = 25text{ W}$, and the distance from the point to the source is $r = 5.1text{ m}$.

Now using formula (1) we find the intensity as follows:

$$
begin{align*}
I = frac{P}{4 , r^2 , pi}
end{align*}
$$

Plugging in the values we get:

$$
begin{align*}
I = frac{25text{ W}}{4 , (5.1text{ m})^2 , pi} approx 0.077 ; frac{text{W}}{text{m}^2}
end{align*}
$$

Result
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The intensity is $I = 0.077 ; frac{text{W}}{text{m}^2}$
Exercise 59
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The concept is that an increase of 10 dB intensity level requires a 10 times increase in sound intensity. Therefore, to increase the intensity by 10 dB, you need 10 car horns sounding simultaneously.
Result
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10 car horns
Exercise 60
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The concept is that an increase of 10 dB intensity level requires a 10 times increase in sound intensity. So, 20 dB corresponds to 100 increase in sound power.

100 violins will have 100 times the power of 1 violin.

Therefore, a single violin produced 20 dB quitter than 100 violins.

The difference in intensity level is

$$
difference=76 ;dB-20;dB=56;dB
$$

Result
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56 dB
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