Download Doppler effect and resolution worksheet

Doppler effect and resolution:
1.
Which of the following wave phenomena is associated with blood flow measurements?
A.
Polarization
B.
Diffraction
C.
Refraction
D.
Doppler effect
(Total 1 mark)
2.
A radar speed gun is used to measure the speed of a car. The car is moving with speed v away from the gun.
The radar emits microwaves of frequency f and speed c. Which of the following is the frequency of the
microwaves measured at the gun after reflection by the car?
A.
 2v 
f+ 
f
 c 
B.
v 
f+  f
c 
C.
 2v 
f
f– 
 c 
D.
v 
f–  f
c 
(Total 1 mark)
3.
This question is about radio waves.
A satellite is travelling directly away from a space shuttle with a speed of 7.9 km s–1.
The satellite is transmitting radio waves of frequency 150.000 000 MHz.
(a)
(i)
Calculate the frequency to which an astronaut on the shuttle will need to set a receiver in order
to receive the signal from the satellite.
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(2)
(ii)
The satellite now passes close to a second space shuttle. Describe the changes that will need to
be made to the setting of the receiver as the satellite approaches and moves away from the
second shuttle.
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(3)
(iii)
Suggest why the formula used in the calculation in (a)(i) would not be suitable for radiation
from a distant galaxy moving away from the Earth at 90 % of the speed of light.
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(1)
(b)
A space shuttle orbits at a height of 300 km above the surface of the Earth. It carries two panels
separated by a distance of 24 m. The panels reflect light of wavelength 500 nm towards an observer on
the Earth’s surface.
The observer views the panels with a telescope of aperture diameter 85 mm. The panels act as point
sources of light for the observer.
(i)
Describe what is meant by the Rayleigh criterion.
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(2)
(ii)
Determine whether the images of the panels formed by the telescope will be resolved.
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(3)
(Total 11 marks)
4.
A man standing by the shore observes sea waves approaching at a frequency of 0.20 Hz. A man on a boat observes
that waves are approaching the boat at a frequency of 0.50 Hz. The speed of the waves is 2.0 m s–1. Which of
the following gives a possible value for the speed of the boat and its direction?
Speed / m s–1
Direction
A.
3.0
away from the shore
B.
3.0
towards the shore
C.
1.2
away from the shore
D.
1.2
towards the shore
(Total 1 mark)
5.
A source of sound approaches a stationary observer. The speed of the emitted sound and its wavelength,
measured at the source, are v and λ respectively. Which of the following is the wave speed and the
wavelength, as measured by the stationary observer?
Wave speed
Wavelength
A.
larger than v
larger than λ
B.
equal to v
larger than λ
C.
equal to v
less than λ
D.
larger than v
less than λ
(Total 1 mark)
Answers:
1. D
2. C
3.
(a)
(i)
v

∆f =  × 150 × 10 6 
c

= 3950Hz;
= 149.99605 MHz;
(ii)
(b)
2
as approaches frequency greater than 150 MHz/higher than
transmission frequency;
when opposite shuttle frequency 150 MHz/same as
transmission frequency;
as recedes frequency lower than 150 MHz/lower than
transmission frequency;
3
(iii)
equation only applies for v << c / relativistic effects occur (at 0.9c);
1
(i)
the Rayleigh Criterion is used to establish when the image
of two objects are just resolved / Rayleigh criterion describes
resolution condition;
the minimum of one diffraction pattern falls on the maximum
of the other;
2
(ii)
1.22λ 

 use of θ =

d 

resolution = 1.22 ×
5 × 10 −7
8.5 × 10
−2
= 7.2 × 10–6 rad;

 24 × 10
θ = 
=  80 × 10–6 (rad);

 300
separation > resolution limit so can be resolved;
Allow ecf for third marking point.
−3
3
[11]
4. A
5. C