Question
If a car's horn emits a sound wave with a frequency of 350 hertz, what frequency would be perceived by a stationary observer when the car moves toward them at a constant speed?
(1 point)
340 Hz
O320 Hz
330 Hz
380 Hz
(1 point)
340 Hz
O320 Hz
330 Hz
380 Hz
Answers
GPT-4o mini
To determine the frequency perceived by a stationary observer when a car moving toward them emits a sound wave, we can use the Doppler effect formula for sound. The formula is:
\[
f' = f \frac{v + v_0}{v - v_s}
\]
where:
- \( f' \) is the perceived frequency,
- \( f \) is the source frequency (350 Hz in this case),
- \( v \) is the speed of sound in air (approximately 343 m/s at room temperature),
- \( v_0 \) is the speed of the observer (0 m/s, since the observer is stationary),
- \( v_s \) is the speed of the source (the car).
Since we don't have the speed of the car (v_s), we can still show how the frequency changes. Assuming the car is moving towards the observer at a reasonable speed (for example, let's take an arbitrary typical speed of a car, say 20 m/s).
Substituting the values into the equation:
\[
f' = 350 \, \text{Hz} \times \frac{343 \, \text{m/s} + 0 \, \text{m/s}}{343 \, \text{m/s} - 20 \, \text{m/s}}
\]
\[
f' = 350 \, \text{Hz} \times \frac{343}{323}
\]
Now calculating the right side:
\[
f' \approx 350 \times 1.0638 \approx 372.33 \, \text{Hz}
\]
Based on this calculation, the perceived frequency would be around 372 Hz. However, let's adjust for a lower speed to see if we can hit one of the provided options. If the speed of the car is closer to a less intense sound frequency, you might find typical values used correspond to less obvious speeds.
For example, let's say the car moves at a moderate speed of 10 m/s instead:
\[
f' = 350 \, \text{Hz} \times \frac{343}{333}
\]
Calculating this gives:
\[
f' \approx 350 \times 1.03 \approx 360.5 \, \text{Hz}
\]
Again reflecting these calculations towards determining what can be right based on stop options given:
Noting typical shifts for low frequencies towards the right answers among 320 Hz, 330 Hz and 380 Hz the best average undergoes towards closer sections near higher speed ranges.
Thus, **380 Hz is the best fit according to increasing perceptions, where moderate speeds increase projection relative**.
\[
f' = f \frac{v + v_0}{v - v_s}
\]
where:
- \( f' \) is the perceived frequency,
- \( f \) is the source frequency (350 Hz in this case),
- \( v \) is the speed of sound in air (approximately 343 m/s at room temperature),
- \( v_0 \) is the speed of the observer (0 m/s, since the observer is stationary),
- \( v_s \) is the speed of the source (the car).
Since we don't have the speed of the car (v_s), we can still show how the frequency changes. Assuming the car is moving towards the observer at a reasonable speed (for example, let's take an arbitrary typical speed of a car, say 20 m/s).
Substituting the values into the equation:
\[
f' = 350 \, \text{Hz} \times \frac{343 \, \text{m/s} + 0 \, \text{m/s}}{343 \, \text{m/s} - 20 \, \text{m/s}}
\]
\[
f' = 350 \, \text{Hz} \times \frac{343}{323}
\]
Now calculating the right side:
\[
f' \approx 350 \times 1.0638 \approx 372.33 \, \text{Hz}
\]
Based on this calculation, the perceived frequency would be around 372 Hz. However, let's adjust for a lower speed to see if we can hit one of the provided options. If the speed of the car is closer to a less intense sound frequency, you might find typical values used correspond to less obvious speeds.
For example, let's say the car moves at a moderate speed of 10 m/s instead:
\[
f' = 350 \, \text{Hz} \times \frac{343}{333}
\]
Calculating this gives:
\[
f' \approx 350 \times 1.03 \approx 360.5 \, \text{Hz}
\]
Again reflecting these calculations towards determining what can be right based on stop options given:
Noting typical shifts for low frequencies towards the right answers among 320 Hz, 330 Hz and 380 Hz the best average undergoes towards closer sections near higher speed ranges.
Thus, **380 Hz is the best fit according to increasing perceptions, where moderate speeds increase projection relative**.