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14 Mar 2020
The Doppler Effect As a train moves upward an observer (see the figure), the pitch of its whistle sounds higher to the observer than it would if the train were at rest, because the crests of the sound waves are compressed closer together. This phenomenon is called the Doppler Effect. The observed pitch
is a function of the speed
of the train and is given by
![](data:image/png;base64,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)
where
is the actual pitch of the whistle at the source and
m/s is the speed of sound in the air. Suppose that a train has a whistle pitched at
Hz. Graph the function
using a graphing device. How can the vertical asymptote of this function be interpreted physically?
![](data:image/png;base64,)
The Doppler Effect As a train moves upward an observer (see the figure), the pitch of its whistle sounds higher to the observer than it would if the train were at rest, because the crests of the sound waves are compressed closer together. This phenomenon is called the Doppler Effect. The observed pitch is a function of the speed
of the train and is given by
where is the actual pitch of the whistle at the source and
m/s is the speed of sound in the air. Suppose that a train has a whistle pitched at
Hz. Graph the function
using a graphing device. How can the vertical asymptote of this function be interpreted physically?
Hubert KochLv2
29 May 2020