A turning fork vibrating at `500 Hz` falls from rest accelerates at `10 m//s^(2)`.
Velocity of the tuning fork when waves with a frequency of `475 Hz` reach the release point is ( Take the speed of sound in air to be `340 m//s`).

Options

A. `1.79 m//s`
B. `17.9 m//s`
C. `35.8 m//s`
D. `3.58 m//s`

Explanation

To solve the problem step by step, we will use the formula for the apparent frequency in the Doppler effect:

### Step 1: Understand the given information
- Frequency of the tuning fork (f) = 500 Hz
- Apparent frequency (f') = 475 Hz
- Speed of sound in air (v) = 340 m/s
- Initial velocity of the observer (vo) = 0 m/s (since the observer is at the release point)
- The tuning fork is falling with an acceleration of 10 m/s².

### Step 2: Use the Doppler effect formula
The formula for the apparent frequency when the source is moving away from the observer is given by:

\[ f' = f \frac{v + v_o}{v - v_s} \]

Where:
- \( f' \) = apparent frequency
- \( f \) = actual frequency of the source
- \( v \) = speed of sound
- \( v_o \) = velocity of the observer
- \( v_s \) = velocity of the source (tuning fork)

### Step 3: Substitute known values into the formula
Substituting the known values into the equation:

\[ 475 = 500 \frac{340 + 0}{340 - v_s} \]

### Step 4: Simplify the equation
This simplifies to:

\[ 475 = 500 \frac{340}{340 - v_s} \]

### Step 5: Cross-multiply to eliminate the fraction
Cross-multiplying gives:

\[ 475(340 - v_s) = 500 \times 340 \]

### Step 6: Expand and rearrange the equation
Expanding the left side:

\[ 161500 - 475v_s = 170000 \]

Now, rearranging to solve for \( v_s \):

\[ -475v_s = 170000 - 161500 \]

\[ -475v_s = 8500 \]

### Step 7: Solve for \( v_s \)
Dividing both sides by -475:

\[ v_s = \frac{8500}{475} \approx 17.89 \text{ m/s} \]

### Conclusion
The velocity of the tuning fork when the waves with a frequency of 475 Hz reach the release point is approximately **17.89 m/s**.