P18_056.PDF

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Chapter 18 - 18.56
56. The Doppler shift formula, Eq. 18-47, is valid only when both u S and u D are measured with respect to
a stationary medium (i.e., no wind). To modify this formula in the presence of a wind, we switch to a
new reference frame in which there is no wind.
(a) When the wind is blowing from the source to the observer with a speed w ,wehave u S = u D = w in
the new reference frame that moves together with the wind. Since the observer is now approaching
thesourcewhilethesourceisbackingofffromtheobserver,wehave,inthenewreferenceframe,
f = f v + u D
v + u S
= f v + w
v + w
= 2000 Hz .
In other words, there is no Doppler shift.
(b) In this case, all we need to do is to reverse the signs in front of both u D and u S . The result is that
there is still no Doppler shift:
f = f v
−
u D
= f v
−
w
= 2000 Hz .
v
−
u S
v
−
w
In general, there will always be no Doppler shift as long as there is no relative motion between the
observer and the source, regardless of whether a wind is present or not.

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