The frequency of a tunning fork is 384 per second and velocity of sound in air is 352 m/s . How far the sound has traversed while fork completes 36 vibration

Options

A. 33m
B. 16.5 m
C. 11 m
D. 22 m

Answer

To solve the problem, we need to find out how far sound travels while a tuning fork completes 36 vibrations. We will use the given frequency of the tuning fork and the speed of sound in air.

### Step-by-Step Solution:

1. **Identify the given values:**
- Frequency of the tuning fork (f) = 384 Hz (vibrations per second)
- Velocity of sound in air (v) = 352 m/s
- Number of vibrations (n) = 36

2. **Calculate the time for one vibration:**
The time period (T) for one vibration can be calculated using the formula:
\[ T = \frac{1}{f} \]
Substituting the given frequency:
\[ T = \frac{1}{384} \text{ seconds} \]

3. **Calculate the total time for 36 vibrations:**
The total time (t) for 36 vibrations is:
\[ t = n \times T = 36 \times \frac{1}{384} \]
Simplifying this:
\[ t = \frac{36}{384} = \frac{1}{10.67} \text{ seconds} \approx 0.0336 \text{ seconds} \]

4. **Calculate the distance traveled by sound:**
The distance (d) traveled by sound can be calculated using the formula:
\[ d = v \times t \]
Substituting the values of velocity and time:
\[ d = 352 \times \frac{36}{384} \]
Simplifying this:
\[ d = 352 \times 0.09375 \approx 33 \text{ meters} \]

5. **Final Answer:**
The distance traveled by sound while the fork completes 36 vibrations is approximately **33 meters**.