18IB Doppler
[21 marks]
1. Sea waves move towards a beach at a constant speed of 2.0 m s–1. They [1 mark]
arrive at the beach with a frequency of 0.10 Hz. A girl on a surfboard is
moving in the sea at right angles to the wave fronts. She observes that the
surfboard crosses the wave fronts with a frequency of 0.40 Hz.
What is the speed of the surfboard and what is the direction of motion of the
surfboard relative to the beach?
2. A train approaches a station and sounds a horn of constant frequency and [1 mark]
constant intensity. An observer waiting at the station detects a frequency
fobs and an intensity Iobs. What are the changes, if any, in Iobs and fobs as the train
slows down?
3. An ambulance siren emits a sound of frequency 1200 Hz. The speed of
[1 mark]
sound in air is 330 m s–1. The ambulance moves towards a stationary
observer at a constant speed of 40 m s–1. What is the frequency heard by the
observer?
A.
B.
C.
D.
1200×330
Hz
370
1200×290
Hz
330
1200×370
Hz
330
1200×330
Hz
290
4. A stationary sound source emits waves of wavelength λ and speed v. The [1 mark]
source now moves away from a stationary observer. What are the
wavelength and speed of the sound as measured by the observer?
5. A train moving at speed u relative to the ground, sounds a whistle of
constant frequency f as it moves towards a vertical cliff face.
[1 mark]
The sound from the whistle reaches the cliff face and is reflected back to the train.
The speed of sound in stationary air is c.
What whistle frequency is observed on the train after the reflection?
A.
(c+u)
f
(c−u)
B. (c + u)f
C. (c – u)f
D.
(c−u)
f
(c+u)
6. A train travelling in a straight line emits a sound of constant frequency f. [1 mark]
An observer at rest very close to the path of the train detects a sound of
continuously decreasing frequency. The train is
A. approaching the observer at constant speed.
B. approaching the observer at increasing speed.
C. moving away from the observer at constant speed.
D. moving away from the observer at increasing speed.
7a. Police use radar to detect speeding cars. A police officer stands at the
[6 marks]
side of the road and points a radar device at an approaching car. The
device emits microwaves which reflect off the car and return to the device. A
change in frequency between the emitted and received microwaves is measured
at the radar device.
The frequency change Δ f is given by
Δf =
2fv
c
where f is the transmitter frequency, v is the speed of the car and c is the wave
speed.
The following data are available.
Transmitter frequency f = 40 GHz Δf = 9.5 kHz Maximum speed allowed = 28 m s–
1
(i) Explain the reason for the frequency change.
(ii) Suggest why there is a factor of 2 in the frequency-change equation.
(iii) Determine whether the speed of the car is below the maximum speed allowed.
7b. Airports use radar to track the position of aircraft. The waves are
[2 marks]
reflected from the aircraft and detected by a large circular receiver. The
receiver must be able to resolve the radar images of two aircraft flying close to
each other.
The following data are available.
Diameter of circular radar receiver = 9.3 m Wavelength of radar = 2.5 cm
Distance of two aircraft from the airport = 31 km
Calculate the minimum distance between the two aircraft when their images can
just be resolved.
8. A train moves at constant speed whilst emitting a sound wave of
[1 mark]
frequency f0. At t=t0 the train passes through a station. Which graph
shows the variation with time t of the frequency f of the sound wave as measured
by an observer standing on the station platform?
9. An object emitting a sound of frequency 100 Hz orbits in a horizontal
circle at a rate of two revolutions per second.
[1 mark]
An observer standing a short distance away from the object is able to hear the
sound. Which of the following describes the sound the observer is able to hear?
A. A sound of constant frequency but varying in amplitude
B. A sound of constantly varying frequency
C. A sound with a frequency of 50 Hz
D. A sound with a frequency of 200 Hz
This question is about the Doppler effect.
The diagram shows wavefronts in air produced by a stationary source S of sound.
The distance between successive wavefronts is equal to the wavelength of the
sound. The speed of sound is c.
10a. On the diagram, sketch three successive wavefronts produced when S [2 marks]
is moving to the left at a speed of 0.5 c.
10b. A source of X-rays rotates on a turntable. Radiation of wavelength 7.5 [3 marks]
nm is emitted by the source and undergoes a maximum shift of 0.50
fm. The distance between the source and the detector is large in comparison to
the diameter of the turntable.
(i) Determine the speed of a point on the edge of the turntable.
(ii) State the assumption you made in your answer to (b)(i).
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