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Doppler Effect for sound waves

Doppler Effect for sound waves. Consider a source emitting a sound wave of speed v and frequency f . The oscillation period is T = 1/ f . A sound wave is a “train” of compressions and rarefactions. Let’s focus our eyes on one “compression” and see how it moves:. Initial situation

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Doppler Effect for sound waves

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  1. Doppler Effect for sound waves

  2. Consider a source emitting a sound wave of speed v and frequency f. The oscillation period is T = 1/f. A sound wave is a “train” of compressions and rarefactions. Let’s focus our eyes on one “compression” and see how it moves: Initial situation One period T later Two periods T later In each time period T the “compression” moves ahead by one wavelength  .

  3. As in the preceding • slide: the source • emits a “compression”… • …After one period T it’s • moved away by , and • a next “compression” • emerges from the source. • (b) Consider a similar situ- • ation: the source emits • sound of the same f as • before, but now it moves • with speed vs . • Because now the source • “chases” the “compres- • sion”, the next one is • created closer to it by vsT . • In other words, the wavelength • from the moving source is • shortened by vsT . The “compression” moves away from the source with the same speed as in (a).

  4. The change of frequency due to the source motion is known as the Doppler Effect. From the formula we derived it follows that if the source moves toward the observer, the frequqency recorded by him/her is higher than f0 , the oscillation frequency of the source: If the source moves away from the obsever, (receding source), one can think of it as of “approaching with negative speed”, so we have to change the sign of the source’s speed. The frequency recorded is now lower than f0 :

  5. Doppler: observer’s motion. A. The observer does not move. After one “com- pression” reaches her ear, a time T=1/f0 passes until the next one (marked red) does. B. Now the observer is moving, approaching the source. After one “com- pression reaches her ear, the next one does after a shorter time T’ passes than in the first case. She hears a sound with frequency f+ = 1/T’. From the plot, it can be readily seen that: v vo v vo

  6. So, the “Doppler shifted frequencies” due to the observer’s motion are: The frequency recorded by a stationary observer is equal to the source oscillation frequency f0 if the source is stationary, but if the source moves, then the frequencies heard by a static observer are those in Slide 4. Combining, we obtain an universal formula for situations in which the observer and the source are both in motion: The upper sign in each combination means “approaching”; the lower one means “receding”.

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