18IB Doppler [21 marks]

1. Sea waves move towards a beach at a constant speed of 2.0 m s . Theyarrive at the beach with a frequency of 0.10 Hz. A girl on a surfboard ismoving in the sea at right angles to the wave fronts. She observes that thesurfboard 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 thesurfboard relative to the beach?

MarkschemeB

Examiners report[N/A]

–1 [1 mark]

2. A train approaches a station and sounds a horn of constant frequency andconstant intensity. An observer waiting at the station detects a frequencyf and an intensity I . What are the changes, if any, in I and f as the trainslows down?

MarkschemeD

Examiners reportAn unusual way of considering the Doppler effect, this had a very lowdiscrimination index with the most popular answer A when D was correct. It islikely the candidates have confused what the train is producing – a constantintensity sound – and what the observer hears, Io, where the intensity is goingto increase as the train approaches. This immediately eliminates options A andC.

obs obs obs obs

[1 mark]

3. An ambulance siren emits a sound of frequency 1200 Hz. The speed ofsound in air is 330 m s . The ambulance moves towards a stationaryobserver at a constant speed of 40 m s . What is the frequency heard by theobserver? A. Hz

B. Hz

C. Hz

D. Hz

MarkschemeD

Examiners report[N/A]

–1–1

1200×330370

1200×290330

1200×370330

1200×330290

4. A stationary sound source emits waves of wavelength and speed v. Thesource now moves away from a stationary observer. What are thewavelength and speed of the sound as measured by the observer?

MarkschemeA

Examiners report[N/A]

λ

[1 mark]

[1 mark]

5. A train moving at speed u relative to the ground, sounds a whistle ofconstant frequency f as it moves towards a vertical cliff face.

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.

B. (c + u)fC. (c – u)f

D.

MarkschemeA

Examiners report[N/A]

f(c+u)(c−u)

f(c−u)(c+u)

6. A train travelling in a straight line emits a sound of constant frequency f.An observer at rest very close to the path of the train detects a sound ofcontinuously decreasing frequency. The train isA. 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.

[1 mark]

[1 mark]

MarkschemeD

Examiners report[N/A]

7a. Police use radar to detect speeding cars. A police officer stands at theside of the road and points a radar device at an approaching car. Thedevice emits microwaves which reflect off the car and return to the device. Achange in frequency between the emitted and received microwaves is measuredat the radar device.The frequency change Δf is given by

where f is the transmitter frequency, v is the speed of the car and c is the wavespeed.The following data are available.Transmitter frequency f = 40 GHz Δf = 9.5 kHz Maximum speed allowed = 28 m s

(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.

Δf =2fv

c

–1

[6 marks]

Markschemeimention of Doppler effectOR«relative» motion between source and observer producesfrequency/wavelength changeAccept answers which refer to a double frequency shift.Award [0] if there is any suggestion that the wave speed is changed in theprocess.

the reflected waves come from an approaching “source” ORthe incident waves strike an approaching “observer”increased frequency received «by the device or by the car»

iithe car is a moving “observer” and then a moving “source”, so the Dopplereffect occurs twiceORthe reflected radar appears to come from a “virtual image” of the devicetravelling at 2 v towards the device iiiALTERNATIVE 1For both alternatives, allow ecf to conclusion if v OR Δf are incorrectlycalculated.

v = « » 36 «ms »

«36> 28» so car exceeded limitThere must be a sense of a conclusion even if numbers are not quoted.ALTERNATIVE 2reverse argument using speed limit.

« » 7500 «Hz»

« 9500> 7500» so car exceeded limitThere must be a sense of a conclusion even if numbers are not quoted.

Examiners report[N/A]

=(3×108)×(9.5×103)

(40×109)×2–1

Δf = =2×40×109×283×108

7b. Airports use radar to track the position of aircraft. The waves arereflected from the aircraft and detected by a large circular receiver. Thereceiver must be able to resolve the radar images of two aircraft flying close toeach other.The following data are available.Diameter of circular radar receiver = 9.3 m Wavelength of radar = 2.5 cmDistance of two aircraft from the airport = 31 km Calculate the minimum distance between the two aircraft when their images canjust be resolved.

MarkschemeAward [2] for a bald correct answer.Award [1 max] for POT error.100 «m»Award [1 max] for 83m (omits 1.22).

Examiners report[N/A]

x = 31×103×1.22×2.5×10−2

9.3

[2 marks]

8. A train moves at constant speed whilst emitting a sound wave offrequency f . At t=t the train passes through a station. Which graphshows the variation with time t of the frequency f of the sound wave as measuredby an observer standing on the station platform?

MarkschemeD

Examiners report[N/A]

0 0[1 mark]

9. An object emitting a sound of frequency 100 Hz orbits in a horizontalcircle at a rate of two revolutions per second.

An observer standing a short distance away from the object is able to hear thesound. Which of the following describes the sound the observer is able to hear?A. A sound of constant frequency but varying in amplitudeB. A sound of constantly varying frequencyC. A sound with a frequency of 50 HzD. A sound with a frequency of 200 Hz

MarkschemeB

Examiners report[N/A]

[1 mark]

10a.

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 thesound. The speed of sound is c.

On the diagram, sketch three successive wavefronts produced when Sis moving to the left at a speed of 0.5c.

[2 marks]

Markscheme3 circular wavefronts;2 centres/sources of wavefronts move left (by one box);

Drawn circular wavefronts may be larger as in diagram here, or could be equalsized. Both are acceptable.

Examiners report[N/A]

© International Baccalaureate Organization 2020 International Baccalaureate® - Baccalauréat International® - Bachillerato Internacional®

10b. A source of X-rays rotates on a turntable. Radiation of wavelength 7.5nm 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 tothe 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).

Markscheme(i) ;20(ms-1);Use of sound equation not acceptable.(ii) assume speed of X-rays c / assume speed of turntable << c;

Examiners report[N/A]

v = 5×10−16×3×108

7.5×10−9

=

[3 marks]

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