Physics
Physics
1st Edition
Walker
ISBN: 9780133256925
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Page 514: Practice Problems

Exercise 47
Step 1
1 of 2
The intensity of sound wave is defined as the ratio power delivered by the wave and the area through which it travels. If both the power and area is doubled, then the intensity remains constant.
Result
2 of 2
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Exercise 48
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:

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

Step 2
2 of 3
### Calculation

We know that the power of the sound source is $P = 0.21text{ W}$. To find the area through which it has to pass to have an intensity $I = 0.067 ; frac{text{W}}{text{m}^2}$ is done simply, using formula (1) as follows:

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

Rearranging for $A$:

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

Plugging in the values we get:

$$
begin{align*}
A = frac{0.21text{ W}}{0.067 ; frac{text{W}}{text{m}^2}} approx 3.1text{ m}^2
end{align*}
$$

Result
3 of 3
The area the sound wave passes through is $A = 3.1text{ m}^2$
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