https://file.aiquickdraw.com/mathbot/file/1727198400187h36qmq62.jpg

The provided image contains a problem related to sound intensity and sound intensity level in decibels (dB). Let's break it down and solve the two questions:

---

### Given Information:

- **Intensity formula**:  
  The intensity level \( L \) in decibels (dB) is given by:
  \[
  L = 10 \log \left(\frac{I}{I_0}\right)
  \]
  where:
  - \( I \) is the sound intensity in \( \text{W/m}^2 \),
  - \( I_0 = 10^{-12} \, \text{W/m}^2 \) (threshold of hearing).

---

### Part (a):
**Question:** The sound intensity of a chainsaw at a distance of 1 meter is \( 0.1 \, \text{W/m}^2 \). What is the sound intensity level?

#### Solution:
We are given \( I = 0.1 \, \text{W/m}^2 \). Substituting this into the formula:

\[
L = 10 \log \left(\frac{0.1}{10^{-12}}\right)
\]

Let me calculate this for you.The sound intensity level for the chainsaw at a distance of 1 meter is \( 110 \, \text{dB} \).

---

### Part (b):
**Question:** When there are two chainsaws, the sound intensity doubles. By how many decibels does the sound intensity level increase?

#### Solution:
When the intensity doubles, the new intensity \( I' = 2 \times 0.1 \, \text{W/m}^2 = 0.2 \, \text{W/m}^2 \).

Now, let's calculate the new intensity level \( L' \) using:
\[
L' = 10 \log \left(\frac{0.2}{10^{-12}}\right)
\]

The increase in decibels is \( \Delta L = L' - L \).

Let me compute that for you.The increase in sound intensity level when the number of chainsaws doubles is approximately \( 3.01 \, \text{dB} \).

---

### Summary of Results:
1. The sound intensity level for a single chainsaw is \( 110 \, \text{dB} \).
2. When the sound intensity doubles (due to two chainsaws), the intensity level increases by approximately \( 3.01 \, \text{dB} \).

Would you like further details or clarifications?

---

Here are 5 related questions you might be interested in:
1. How do different frequencies affect the perception of loudness in dB?
2. What are the implications of sound intensity levels on hearing damage?
3. How does sound intensity decrease as you move further from the source?
4. What is the effect of adding more sound sources (like multiple chainsaws) on overall loudness?
5. How does sound absorption in different environments affect intensity levels?

**Tip:** Every increase of 10 dB corresponds to a tenfold increase in sound intensity, but only about a twofold increase in perceived loudness.

a) Moottorisahan äänen intensiteetti metrin etäisyydellä on 0,1 W/m². Kuinka suuri on äänen intensiteettitaso? b) Kun moottorisahoja on kaksi, niin äänen intensiteetti kaksinkertaistuu. Kuinka monta desibeliä nousee äänen intensiteettitaso?

Learn how to calculate the sound intensity level in decibels for a chainsaw at a distance of 1 meter with an intensity of 0.1 W/m², and how the intensity level increases when the number of chainsaws doubles. Includes key logarithmic formulas for sound intensity calculation.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation