Problem 1 (10 points) Imagine a sound source is moving away from an observer with speed vs(>0) and the observer is chasi

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Problem 1 10 Points Imagine A Sound Source Is Moving Away From An Observer With Speed Vs 0 And The Observer Is Chasi 1 (231.62 KiB) Viewed 31 times

Problem 1 (10 points) Imagine a sound source is moving away from an observer with speed vs(>0) and the observer is chasing the source with speed v.(> 0). When the source is emitting a sound with frequency f, the frequency f' that the observer hears is Cg + vo f' ?f, (1) Cgt Us for the sound speed Cs. This is called the classical (or non-relativistic) Doppler effect and it's actually only an approximation to the relativistic Doppler effect: = Cs 1-B Us – Vo V1+B (2) Notice that the relativistic one only depends on the relative speed vs – v, instead of the individual ones vs and v.. Let's check that the relativistic and classical Doppler effects agree when Vs and v, are much smaller than Cs. (a) When |2 <1, the following approximation holds: (1 + x)" ~1+nz. (3) Use this to show that the classical Doppler formula in Eq. (1) becomes Us - Vo 1 - Cs fi (4) when throwing away terms that are speed squared (including vsvo) and higher. (Hint: This problem is similar to written HW4 Prob 1(b).] (b) Similarly, use Eq. (3) to show that the relativistic Doppler formula in Eq. (2) also reduces to Eq. (4) when throwing away terms that are speed squared and higher. (This completes the proof that the two formulas are equivalent when vs and v, are smaller than Cs.)