To determine the apparent frequency recorded by the receiver when the source is moving away from it, we can use the Doppler effect formula for sound. The Doppler effect describes how the frequency of a wave changes for an observer moving relative to the source of the wave. In this case, since the source is accelerating away from the receiver, we need to consider both the initial frequency and the change in distance over time.
Understanding the Doppler Effect
The formula for the apparent frequency \( f' \) when the source is moving away from a stationary observer is given by:
f' = f \times \frac{v}{v + v_s}
Where:
- f' = apparent frequency
- f = source frequency (1700 kHz)
- v = speed of sound in air (340 m/s)
- v_s = speed of the source relative to the observer
Calculating the Speed of the Source
Since the source starts from rest and accelerates, we can calculate its speed at \( t = 10 \) seconds using the formula:
v_s = a \times t
Substituting the values:
v_s = 10 \, \text{m/s}^2 \times 10 \, \text{s} = 100 \, \text{m/s}
Finding the Apparent Frequency
Now that we have the speed of the source, we can substitute the values into the Doppler effect formula:
f' = 1700 \, \text{kHz} \times \frac{340 \, \text{m/s}}{340 \, \text{m/s} + 100 \, \text{m/s}}
Calculating the denominator:
340 + 100 = 440 \, \text{m/s}
Now substituting back into the formula:
f' = 1700 \, \text{kHz} \times \frac{340}{440}
Calculating the fraction:
f' = 1700 \, \text{kHz} \times 0.7727 \approx 1312.73 \, \text{kHz}
Final Result
Thus, the apparent frequency recorded by the receiver at \( t = 10 \) seconds is approximately 1312.73 kHz. This decrease in frequency occurs because the source is moving away from the receiver, causing the waves to stretch and the frequency to drop.
