A small asteroid of mass M is near a big asteroid of mass 3M. There are no other gravitating objects nearby. The magnitudes of t
he accelerations of the big and small asteroids are aBig and asmall, respectively. What is the ratio of the magnitudes of the accelerations (aBig/ asmall)?
1 answer:
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(a) 1440.5 Hz
The general formula for the Doppler effect is
where
f is the original frequency
f is the apparent frequency
is the velocity of the wave
is the velocity of the receiver (positive if the receiver is moving towards the source, negative otherwise)
is the velocity of the source (positive if the source is moving away from the receiver, negative otherwise)
Here we have
f = 1110 Hz
v = 334 m/s
In the reflector frame (= on surface B), we have also
(surface A is the source, which is moving towards the receiver)
(surface B is the receiver, which is moving towards the source)
So, the frequency observed in the reflector frame is
(b) 0.232 m
The wavelength of a wave is given by
where
v is the speed of the wave
f is the frequency
In the reflector frame,
f = 1440.5 Hz
So the wavelength is
(c) 1481.2 Hz
Again, we can use the same formula
In the source frame (= on surface A), we have
(surface B is now the source, since it reflects the wave, and it is moving towards the receiver)
(surface A is now the receiver, which is moving towards the source)
So, the frequency observed in the source frame is
(d) 0.225 m
The wavelength of the wave is given by
where in this case we have
v = 334 m/s
f = 1481.2 Hz is the apparent in the source frame
So the wavelength is