Book 1

p. 220

The Doppler effect

http://www.youtube.com/watch?v=rqehO9yfwTA

Doppler effect… is the change in frequency (or pitch) of the sound detected by a listener because the sound source and the listener have different velocities relative to the medium of sound propagation.

λ

Sound source moving towards observer, frequency is higher.

λ

Sound source moving away from observer, frequency is lower.

λ

Calculations

𝑓𝐿= 𝑣±𝑣𝐿

𝑣±𝑣𝑆𝑓𝑠

LS

fL = frequency of sound heard by the listenerfs = frequency of sound emitted by the sound sourcev = speed of sound in air (340 m.s-1)vs = velocity of the sourcevL = velocity of the listener

Calculations

𝑓𝐿= 𝑣+𝑣𝐿

𝑣−𝑣𝑆𝑓𝑠

Source and observer moving towards each other:f is higher

Factor > 1 ∴ + above the line & – under the line.

Calculations

𝑓𝐿= 𝑣−𝑣𝐿

𝑣+𝑣𝑆𝑓𝑠

Source and observer moving away from each other: f is lower

Factor < 1 ∴ – above the line & + under the line.

Medical applicationDoppler flow meter

The blood velocity through the heart causes a ‘Doppler shift’ in the frequency of the returning waves. The meter measures this and compares the frequencies. The receiver detects the reflected sound and an electronic counter measures the reflected frequency. From the change in frequency, the speed of the blood flow can be determined and narrowing of blood vessels identified.

Medical applicationUltra sound

The movement of the heart in a foetus can be observed from 8-10 weeks after conception.

Application in astronomyRed shift

Red shift is observed when light reaches the earth from most stars. This indicates a shift towards lower frequencies which supports the theory of an expanding universe.

Warm up

Example

𝑓𝐿= 𝑣±𝑣𝐿

𝑣±𝑣𝑆𝑓𝑠

= 340+0

340−15× 1000

= 1 046,15 Hz

The siren of an ambulance emits sound at a frequency of 1 000 Hz. Determine the frequencyof the sound as observed by a stationary observer when the ambulance moves:

(1) At a speed of 15 m.s-1 towards the observer.

Example

𝑓𝐿= 𝑣±𝑣𝐿

𝑣±𝑣𝑆𝑓𝑠

= 340−0

340+15× 1000

= 957,75Hz

The siren of an ambulance emits sound at a frequency of 1 000 Hz. Determine the frequencyof the sound as observed by a stationary observer when the ambulance moves:

(2) At a speed of 15 m.s-1 away from the observer.

Example on steroids

𝑓𝐿 = 𝑣±𝑣𝐿

𝑣±𝑣𝑆𝑓𝑠

266 = 340+0

340−𝑣𝑠× 𝑓𝑠 .......(1)

The graph represents the observed frequencies when a man in the back of a sports vehicle, moving at a constant velocity, blows ona vuvuzela while approaching a stationary traffic cop and then passes this listener. Determine if the driver of the sports vehicle will be fined, if the speed limit is 120 km.h-1. Assume the speed of sound in air is 340 m.s-1.

30

60

90

120

150

180

210

240

270

1 2 3 4 5 6 7t(s)

f(H

z)

210 = 340−0

340+𝑣𝑠× 𝑓𝑠 .......(2)

90 440 - 266vs = 71 400 + 210vs ....... (1) = (2)

vs = 40 m.s-1 = 144 km.h-1

The driver is speeding and will be fined.

Example on steroids

266 = 340+0

340−40× 𝑓𝑠 .......(1)

The graph represents the observed frequencies when a man in the back of a sports vehicle, moving at a constant velocity, blows ona vuvuzela while approaching a stationary traffic cop and then passes this listener. Determine the frequency of the vuvuzela.

30

60

90

120

150

180

210

240

270

1 2 3 4 5 6 7t(s)

f(H

z)

340 fs = 79 800

fs = 234,71 Hz

Substitute vs = 40 m.s-1 into (1)

Beautiful Example

𝑓𝑠= 800 Hz

Learners are measuring the frequency ofa stationary sound source while moving at different velocities away from the source. The results are illustrated in the graph:

1. What is the frequency of the source?

f L(H

z)

100

200

300

400

500

600

700

800

vL (m.s-1)10 205 15

Beautiful Example

𝑔𝑟𝑎𝑑𝑖𝑒𝑛𝑡 = Δ𝑓𝐿

∆𝑣𝐿

= 300−800

20

= 25 m-1

Learners are measuring the frequency of a stationary sound source while moving at different velocities away from the source. The results are illustrated in the graph:

2. What is the gradient of the graph?

f L(H

z)

100

200

300

400

500

600

700

800

vL (m.s-1)10 205 15

Beautiful Example

𝑓𝐿= 𝑣±𝑣𝐿

𝑣±𝑣𝑆𝑓𝑠

= 𝑣 − 𝑣𝐿

𝑣 + 0× 800

= 800 -800

𝑣𝑣𝐿

Learners are measuring the frequency of a stationary sound source while moving at different velocities away from the source. The results are illustrated in the graph:

3. Use the Doppler effect and the gradient of thegraph to calculate the speed of sound in air.

f L(H

z)

100

200

300

400

500

600

700

800

vL (m.s-1)10 205 15

𝑔𝑟𝑎𝑑𝑖𝑒𝑛𝑡 = -800

𝑣

𝑣 = -800

−25= 32 m.s-1

Power gym

p. 224 (Exercise 1)nos. 4, 8, 14(4.4 Assume the train is stationary)

Activity 1p. 236 no. 5

2020/04/13

Please write today's date next to no. 4 on page 224,

but also next to no. 5 on page 236.

4. A train moving at 108 km.h -1, approaches a railway crossing. It warns the pedestrians and motorists thatare waiting at the crossing, by sounding a siren at a frequency of 2 000 Hz.

4.1 Convert 108 km.h -1 to m.s-1

108 𝑘𝑚

1 ℎ= 108 000𝑚

3 600 𝑠= 30 m.s-1

4. A train moving at 108 km.h -1, approaches a railway crossing. It warns the pedestrians and motorists that are waiting at the crossing, by sounding a siren at a frequency of 2 000 Hz.

4.2 Calculate the frequency that the pedestrians hear as the train draws close to the crossing.

𝑓𝐿 = 𝑣±𝑣𝐿

𝑣±𝑣𝑠× 𝑓𝑠

= 340+0

340−30× 2000

= 2 193,55 Hz

4. A train moving at 108 km.h -1, approaches a railway crossing. It warns the pedestrians and motorists that are waiting at the crossing, by sounding a siren at a frequency of 2 000 Hz.

4.3 Calculate the frequency that the pedestrians will hear as the train moves away from the railway crossing.

𝑓𝐿 = 𝑣±𝑣𝐿

𝑣±𝑣𝑠× 𝑓𝑠

= 340−0

340+30× 2000

= 1 837,84 Hz

4. A train moving at 108 km.h -1, approaches a railway crossing. It warns the pedestrians and motorists that are waiting at the crossing, by sounding a siren at a frequency of 2 000 Hz.

4.4 What is the frequency that would be heard by a motorist that is moving at 16 m.s -1 away from thestationary train?

𝑓𝐿 = 𝑣±𝑣𝐿

𝑣±𝑣𝑠× 𝑓𝑠

= 340−16

340+0× 2000

= 1 905,88 Hz

8. The diagram shows how Jane listens to thesound that is emitted from a loudspeakerwhich John, using a rope, swings in a circle ata speed of 30 m.s-1. With the loudspeakerstationary, a frequency of 410 Hz is produced.

8.1 What is the frequency observed by Jane …8.1.1 at A?

𝑓𝐿 = 𝑣±𝑣𝐿

𝑣±𝑣𝑠× 𝑓𝑠

= 340+0

340−30× 410

= 449,68 Hz

8. The diagram shows how Jane listens to thesound that is emitted from a loudspeaker which John, using a rope, swings in a circle at a speed of 30 m.s-1. With the loudspeakerstationary, a frequency of 410 Hz is produced.

8.1 What is the frequency observed by Jane … 8.1.2 at B?

410 Hz

8. The diagram shows how Jane listens to the sound that is emitted from a loudspeaker which John, using a rope, swings in a circle at a speed of 30 m.s-1. With the loudspeakerstationary, a frequency of 410 Hz is produced.

8.1 What is the frequency observed by Jane? …8.1.3 at C?

𝑓𝐿 = 𝑣±𝑣𝐿

𝑣±𝑣𝑠× 𝑓𝑠

= 340−0

340+30× 410

= 376,76 Hz

8. The diagram shows how Jane listens to the sound that is emitted from a loudspeaker which John, using a rope, swings in a circle ata speed of 30 m.s-1. With the loudspeakerstationary, a frequency of 410 Hz is produced.

8.2 What is the frequency observed by John?

410 Hz

14. A bird watcher sitting on a rock, hears the sharpcall of a hawk at a frequency of 700 Hz. Thesound emitted by the hawk has a frequency of900 Hz. The speed of sound on that particular day is 343 m.s-1

14.1 Does the hawk move towards or away from thebird watcher?

Away

14. A bird watcher sitting on a rock, hears the sharp call of a hawk at a frequency of 700 Hz. The sound emitted by the hawk has a frequency of 900 Hz. The speed of sound on that particular day is 343 m.s-1.

14.2 Name the phenomenon that the bird watcher observes.

Doppler effect

14. A bird watcher sitting on a rock, hears the sharpcall of a hawk at a frequency of 700 Hz. Thesound emitted by the hawk has a frequency of 900 Hz. The speed of sound on that particularday is 343 m.s-1

14.3 Calculate how fast the hawk is moving.

𝑓𝐿 = 𝑣±𝑣𝐿

𝑣±𝑣𝑠× 𝑓𝑠

700 = 340−0

340+𝑣𝑠× 900

vs = 98,10 m.s-1

5. Observe the spectra below and answer the following questions. (In each case the upper spectrum is thespectrum of the sun.)

5.1 Which of the galaxies are moving towards us?

5.2 Which of these galaxies are moving away from us?

5.3 Which galaxy is moving away at the highest speed?

5.4 What is the phenomenon called that is observed whena galaxy is approaching us?

5.5 What is the phenomenon called that is observed whena galaxy is moving away from us?

BA & CC

Blue shift

Red shift