A source `S` of acoustic wave of the frequency `v_0=1700Hz` and a receiver `R` are located at the same point. At the instant `t=0`, the source start from rest to move away from the receiver with a constant acceleration `omega`. The velocity of sound in air is `v=340(m)/(s)`.
If `omega=10(m)/(s^2)` for 10s and then `omega=0` for `tgt10s`, the apparent frequency recorded by the receiver at `t=15s`

Options

A. `1700Hz`
B. `1313Hz`
C. `850Hz`
D. `1.23Hz`

Explanation

To solve the problem, we need to determine the apparent frequency recorded by the receiver at \( t = 15 \) seconds, given that the source of sound is moving away from the receiver with a constant acceleration for a certain period.

### Step-by-Step Solution:

1. **Identify Given Data:**
- Frequency of the source, \( v_0 = 1700 \, \text{Hz} \)
- Velocity of sound in air, \( v = 340 \, \text{m/s} \)
- Acceleration of the source, \( \omega = 10 \, \text{m/s}^2 \)
- Time of acceleration, \( t_a = 10 \, \text{s} \)
- Total time, \( t = 15 \, \text{s} \)

2. **Calculate the Velocity of the Source after 10 seconds:**
- The initial velocity \( u = 0 \, \text{m/s} \) (the source starts from rest).
- Using the equation of motion:
\[ v = u + at \]
\[ v = 0 + (10 \, \text{m/s}^2)(10 \, \text{s}) = 100 \, \text{m/s} \]
- Therefore, the velocity of the source at \( t = 10 \, \text{s} \) is \( 100 \, \text{m/s} \).

3. **Determine the Velocity of the Source at \( t = 15 \) seconds:**
- After \( t = 10 \, \text{s} \), the source moves with constant velocity \( v = 100 \, \text{m/s} \).
- Thus, at \( t = 15 \, \text{s} \), the velocity of the source remains \( 100 \, \text{m/s} \).

4. **Apply the Doppler Effect Formula:**
- The formula for apparent frequency \( f' \) when the source is moving away from a stationary observer is:
\[ f' = f_0 \frac{v + v_o}{v + v_s} \]
where:
- \( f_0 = 1700 \, \text{Hz} \) (actual frequency),
- \( v = 340 \, \text{m/s} \) (velocity of sound),
- \( v_o = 0 \, \text{m/s} \) (velocity of the observer),
- \( v_s = 100 \, \text{m/s} \) (velocity of the source).

5. **Substitute Values into the Doppler Effect Formula:**
\[ f' = 1700 \times \frac{340 + 0}{340 + 100} \]
\[ f' = 1700 \times \frac{340}{440} \]
\[ f' = 1700 \times \frac{17}{22} \]
\[ f' = 1700 \times 0.7727 \approx 1313.64 \, \text{Hz} \]

6. **Final Result:**
- The apparent frequency recorded by the receiver at \( t = 15 \, \text{s} \) is approximately \( 1313 \, \text{Hz} \).