"A student stays in a classroom for 5 hours. The noise level in a classroom is 60 dBA. And then he stays in the canteen for 2 hours, wherein the noise level is 105 dBA. Finally, he rides the LRT for 1 hr wherein the noise level is 90 dBA.

a. What will be his noise dose and TWA? (7 points)

b. Is the noise exposure acceptable? (3 points)

### Part A: Noise Dose and Time-Weighted Average (TWA)

To calculate the **Noise Dose** and **Time-Weighted Average (TWA)**, we follow the standards typically used in occupational noise exposure, such as those by OSHA (Occupational Safety and Health Administration). 

First, let's break it down step by step:

#### 1. **Step 1: Noise Dose Formula**
The **noise dose** \( D \) is calculated using:

\[
D = \left( \frac{C_1}{T_1} + \frac{C_2}{T_2} + \frac{C_3}{T_3} + \dots \right) \times 100
\]

Where:
- \( C_1, C_2, \dots \) are the actual time spent in each noise level (in hours).
- \( T_1, T_2, \dots \) are the permissible exposure times for those noise levels (in hours).

The permissible exposure time is the time one can be exposed to a given noise level before exceeding safe limits. OSHA provides the following rule for this:

\[
T = \frac{8}{2^{\left( \frac{L - 90}{5} \right)}}
\]

Where \( T \) is the permissible exposure time in hours and \( L \) is the noise level in dBA.

#### 2. **Step 2: Calculate Permissible Exposure Times**

- **Classroom (60 dBA)**:
  \[
  T_1 = \frac{8}{2^{\left( \frac{60 - 90}{5} \right)}} = \frac{8}{2^{-6}} = 512 \, \text{hours}
  \]
  
- **Canteen (105 dBA)**:
  \[
  T_2 = \frac{8}{2^{\left( \frac{105 - 90}{5} \right)}} = \frac{8}{2^{3}} = \frac{8}{8} = 1 \, \text{hour}
  \]
  
- **LRT (90 dBA)**:
  \[
  T_3 = \frac{8}{2^{\left( \frac{90 - 90}{5} \right)}} = \frac{8}{1} = 8 \, \text{hours}
  \]

#### 3. **Step 3: Calculate Noise Dose**

- Time in classroom: \( C_1 = 5 \) hours
- Time in canteen: \( C_2 = 2 \) hours
- Time in LRT: \( C_3 = 1 \) hour

Now, the noise dose \( D \) is:

\[
D = \left( \frac{5}{512} + \frac{2}{1} + \frac{1}{8} \right) \times 100
\]

Let's calculate that:

\[
D = \left( \frac{5}{512} + 2 + \frac{1}{8} \right) \times 100 = (0.0098 + 2 + 0.125) \times 100 = 2.1348 \times 100 = 213.48\%
\]

So, the **noise dose** is **213.48%**.

#### 4. **Step 4: Calculate Time-Weighted Average (TWA)**
The formula for the **Time-Weighted Average (TWA)** in dBA is:

\[
TWA = 16.61 \log_{10} \left( \frac{D}{100} \right) + 90
\]

Substituting the noise dose:

\[
TWA = 16.61 \log_{10} \left( \frac{213.48}{100} \right) + 90 = 16.61 \log_{10} (2.1348) + 90
\]

\[
TWA = 16.61 \times 0.329 + 90 = 5.46 + 90 = 95.46 \, \text{dBA}
\]

Thus, the **Time-Weighted Average (TWA)** is **95.46 dBA**.

---

### Part B: Is the Noise Exposure Acceptable?

According to OSHA regulations, the permissible TWA for an 8-hour workday is **90 dBA**. Since the student's TWA of **95.46 dBA** exceeds this limit, the noise exposure is **not acceptable**.

---

### Summary of Results:

1. **Noise Dose**: 213.48%
2. **Time-Weighted Average (TWA)**: 95.46 dBA
3. **Is the noise exposure acceptable?**: No, it exceeds the OSHA limit of 90 dBA.

---

### Do you have any questions about this calculation?

#### Related Questions:
1. How does noise dose affect hearing loss risk over time?
2. What are common permissible exposure limits (PEL) for different countries?
3. How is noise dose monitored in industrial environments?
4. Can prolonged exposure to 60 dBA cause hearing damage?
5. What are some ways to reduce noise exposure in high-noise environments?

#### Tip: Always use hearing protection when exposed to noise levels over 85 dBA for prolonged periods.

A student stays in a classroom for 5 hours. The noise level in a classroom is 60 dBA. And then he stays in the canteen for 2 hours, wherein the noise level is 105 dBA. Finally, he rides the LRT for 1 hr wherein the noise level is 90 dBA.

a. What will be his noise dose and TWA? (7 points)

b. Is the noise exposure acceptable? (3 points)

Calculate the noise dose and time-weighted average (TWA) for a student's noise exposure in different environments such as a classroom, canteen, and LRT ride. Using OSHA standards, this example illustrates the key formulas and shows whether the noise exposure is acceptable. Suitable for Grades 10-12.

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