sound: frequency shift when speed of origin is constant

[451617]

this is a problem from kaplan:

"A roller skater carrying a portable stereo skates at constant speed past an observer at rest. Which of the following accurately represents how the frequency perceived by the observer changes with time?"

i chose the graph that is an upside parabola thinking the frequency will increase as the skater approaches the listener and then decrease once the skater is moving past the listener.

the answer they give is one where the frequency is a straight horizontal line followed by a straight vertical line downward and then finally another horizontal line.

the answer explains the frequency is dependent upon the speed of the skater being constant. as skater approaches, the listener hears one frequency higher than from skater's perspective the entire time, and once the skater goes past they hear one frequency lower than skater's perspect.

can someone elaborate on this? i remember TBR or TPR content where i had a similar frequency/doppler shift question in which the correct answer was a parabola. can someone give me an example question where the question WOULD be a parabola so i can note the differences in what both questions are asking?

thanks so much!

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[QrtrLifeCrisis]

this is a problem from kaplan:

"A roller skater carrying a portable stereo skates at constant speed past an observer at rest. Which of the following accurately represents how the frequency perceived by the observer changes with time?"

i chose the graph that is an upside parabola thinking the frequency will increase as the skater approaches the listener and then decrease once the skater is moving past the listener.

the answer they give is one where the frequency is a straight horizontal line followed by a straight vertical line downward and then finally another horizontal line.

the answer explains the frequency is dependent upon the speed of the skater being constant. as skater approaches, the listener hears one frequency higher than from skater's perspective the entire time, and once the skater goes past they hear one frequency lower than skater's perspect.

can someone elaborate on this? i remember TBR or TPR content where i had a similar frequency/doppler shift question in which the correct answer was a parabola. can someone give me an example question where the question WOULD be a parabola so i can note the differences in what both questions are asking?

thanks so much!

Like the answer explained, the key to this question is the constant speed of the skater. Regardless of how far the skater is from the observer, he/she is moving at a constant speed, which would translate into hearing a constant frequency. Once the skater passes the observer, the frequency changes to something lower because of doppler shift. However, the skater is still moving at a constant speed, so the frequency will still be a constant (but lower value than the original). Hence, high horizontal line --> plunge --> low horizontal line.

Correct me if I'm wrong, but I think the parabola example happens if the skater were accelerating towards and away from the observer.