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Step 1. Drawing the Diagram

Step 4. Conclusion

The Problem

We must first draw the diagram of the situation, clearly labeling skater 1, skater 2, their speeds, the frequencies of the horn they hear and the horn itself. Here we see that both skaters are "receivers" of the sound and that skater 1 is moving away while skater 2 is moving towards the horn, and that the horn, the "source" of the sound, is stationary

Once the equations relating frequency heard from the receiver and the frequency emitted at the source are set up for both receivers moving towards and away from the source, the problem becomes one of easy algebra to solve. The main focus of the learning outcome is to explain how we arrive at those equations. The equation is first written solving for the period at the receiver. We start off with this equation because it is familiar to us, we recognize it as the v=(lamba)(f) equation rearranged with the period used instead of frequency. The distinction between a receiver moving away (subtract velocity) and towards (add velocity) the source is then made clear. We then can manipulate this familiar equation into the one we need to solve this new problem.

You are in the final round of the women's singles speed skating event at the winter Olympics. You are in second place approaching the finish line just behind the first place contestant. As the first contestant crosses, a loud horn blows. If you are skating at 13.0 m/s approaching the finish line (where the horn is), and hear the frequency as 660 Hz, what frequency of the horn does the first place contestant hear as they skate away from the finish line with a speed of 13.5 m/s?

Step 3. Setting up the equations

The Doppler Effect: Speed Skating Finals

We will first solve the equation for skater 2, approaching the source (notice the + sign, adding this speed to the speed of the sound wave) as we have 2 of the 3 unknowns needed and can solve for the frequency of sound at the source

We can then use this information to plug into the second equation, which solves for the frequency heard by skater 1.

We then find our answer, the frequency heard by skater 1 is 611Hz

Victoria (Hua) Chen

SN: 31688147

LO5

February 28, 2015

Step 2. Understanding the formula

Physics 101: LO 5

When the source is stationary and the receiver is moving, the period of the receiver, the time it takes for one wave crest to the next to hit the receiver, is equal to the wavelength divided by the speed of the wave. However, since the receiver is moving towards the source, we must add the speed at which the receiver is moving at to the speed of the sound wave. When the receiving is moving away, we must subtract it's speed from the speed of the sound wave.

The wavelength of the sound wave emitted from the source can also be written as velocity divided by frequency of wave at sound source, and the period of the receiver can be written as 1/frequency at the receiver. Rearranging this formula, we end up with our final formula to solve our problem

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