{"id":1840,"date":"2018-04-14T15:33:44","date_gmt":"2018-04-14T07:33:44","guid":{"rendered":"https:\/\/gurumuda.net\/physics\/?p=1840"},"modified":"2023-08-09T08:25:59","modified_gmt":"2023-08-09T08:25:59","slug":"doppler-effect-problems-and-solutions","status":"publish","type":"post","link":"https:\/\/gurumuda.net\/physics\/doppler-effect-problems-and-solutions.htm","title":{"rendered":"Doppler effect \u2013 problems and solutions","gt_translate_keys":[{"key":"rendered","format":"text"}]},"content":{"rendered":"

Doppler effect \u2013 problems and solutions<\/span><\/p>\n

1.<\/span><\/p>\n

(1) an observer moving toward the stationery source<\/span><\/p>\n

(2) source moving toward the stationary observer<\/span><\/p>\n

(3) observer and source approach each other<\/span><\/p>\n

(4) observer and source are moving at the same speed<\/span><\/p>\n

If the pitch heard is higher than that of the emitted source frequency, then which statement <\/span>above are <\/span>correc<\/span>t :<\/span><\/span><\/p>\n

A. (1), (2) and (3)<\/span><\/p>\n

B. (1), (2), (3) and (4)<\/span><\/p>\n

C. (1) and (3)<\/span><\/p>\n

D. (1) and (4)<\/span><\/p>\n

E. (2) and (4)<\/span><\/p>\n

Solution<\/span><\/p>\n

The equation of the Doppler effect<\/a> :<\/span><\/p>\n

\"Doppler<\/span><\/p>\n

Sign rule :<\/span><\/p>\n

The sound speed (v) always positive<\/span><\/p>\n

The observer speed (vobs<\/sub>) is positive if observer moving toward the source of the sound<\/span><\/p>\n

The observer speed (vobs<\/sub>) is negative if the observer moving away from the source of the sound<\/span><\/p>\n

The source speed (vsource<\/sub>) is positive if the source of the sound moving away from the observer<\/span><\/p>\n

The source speed (vsource<\/sub>) is negative if the source of the sound moving toward the observer<\/span><\/p>\n

The observer speed (vobs<\/sub>) = 0 if an observer at rest<\/span><\/p>\n

The source speed (vsource<\/sub>) = 0 if source at rest<\/span><\/p>\n

For example :<\/span><\/p>\n

The observer speed (vobs<\/sub>) = 60 m\/s, if observer at rest then vobs <\/sub>= 0<\/span><\/p>\n

The source speed (vsource<\/sub>) = 40 m\/s, if the source of the sound at rest then vsource<\/sub> = 0<\/span><\/p>\n

The sound speed (v) = 340 m\/s <\/span><\/p>\n

The frequency of sound (f) = 1000 Hertz<\/span><\/p>\n

An observer moving toward the stationery source<\/u><\/span><\/p>\n

The o<\/i>bserver <\/i>speed <\/i>(<\/i>v<\/i>obs<\/i><\/sub>) is<\/i> positive if <\/i>observer moving toward <\/i>the source of the sound<\/i><\/span><\/p>\n

The source of the sound at rest so <\/i>v<\/i>source<\/i> <\/i><\/sub>= 0<\/i><\/span><\/p>\n

\"Doppler<\/span><\/p>\n

Source moving toward the stationary observer<\/u><\/span><\/p>\n

The source speed (vsource<\/sub>) is negative if the source of the sound moving toward an observer<\/i><\/span><\/p>\n

Observer at rest so <\/i>(<\/i>v<\/i>obs<\/i><\/sub>) <\/i>= 0<\/i><\/span><\/p>\n

\"Doppler<\/span><\/p>\n

Observer and source approach each other<\/u><\/span><\/p>\n

The observer speed (vobs<\/sub>) is positive if observer moving toward the source of the sound<\/i><\/span><\/p>\n

The source speed (v<\/i>s<\/i>ource<\/i><\/sub>) is negative if the source of the sound moving toward the observer<\/i><\/span><\/p>\n

\"Doppler<\/span><\/p>\n

Observer and source are moving at the same speed<\/u><\/span><\/p>\n

If the source of the sound and observer moves at the same speed then no Doppler effect occurs.<\/span><\/p>\n

2. An observer at rest near the source of the sound of frequency 684 Hz. Another the source of the sound of 676 Hz moving toward the observer at 2 n\/s. If the speed of the sound waves in air is 340 m\/s, then what is the beat frequency heard by the observer.<\/span><\/p>\n

Known :<\/u><\/span><\/p>\n

The frequency of the source of the sound 1 (f1<\/sub>) = 684 Hz (rest)<\/span><\/p>\n

The frequency of the source of the sound 2 (f2<\/sub>) = 676 Hz (move)<\/span><\/p>\n

The speed of the source of the sound 2 (v2<\/sub>) = 2 m\/s (moving toward the observer)<\/span><\/p>\n

The speed of the source of the sound waves in air (v) = 340 m\/s<\/span><\/p>\n

Wanted:<\/u> The beat frequency heard by the observer<\/span><\/p>\n

Solution :<\/u><\/span><\/p>\n

The equation of the Doppler effect :<\/span><\/p>\n

\"Doppler<\/span><\/p>\n

Sign rule :<\/span><\/p>\n

The sound speed (v) always positive<\/span><\/p>\n

The observer speed (vobs<\/sub>) is positive if observer moving toward the source of the sound<\/span><\/p>\n

The observer speed (vobs<\/sub>) is negative if observer moving away from the source of the sound<\/span><\/p>\n

The source speed (vsource<\/sub>) is positive if the source of the sound moving away from the observer<\/span><\/p>\n

The source speed (vsource<\/sub>) is negative if the source of the sound moving toward the observer<\/span><\/p>\n

The observer speed (vobs<\/sub>) = 0 if an observer at rest<\/span><\/p>\n

The source speed (vsource<\/sub>) = 0 if source at rest<\/span><\/p>\n

\"Doppler<\/span><\/p>\n

The beat frequency heard by the observer = 684 Hz \u2013 680 Hz = 4 Hz.<\/span><\/p>\n

3. A source of sound moving toward the stationary observer at 20 m\/s. The frequency of the source of the sound = 380 Hz. The speed of the sound waves<\/a> in air = 400 m s-1<\/sup>. What is the frequency of the sound waves heard by the observer?<\/span><\/p>\n

Known :<\/u><\/span><\/p>\n

The speed of the source of the sound (vsource<\/sub>) = 20 m\/s<\/span><\/p>\n

The speed of observer (vp<\/sub>) = 0<\/span><\/p>\n

The frequency of the source of the sound (f) = 380 Hz<\/span><\/p>\n

The speed of the source of the sound waves (v) = 400 m s-1<\/sup> <\/span><\/p>\n

Wanted:<\/u> The frequency of the sound waves heard by the observer<\/span><\/p>\n

\"Doppler<\/span><\/p>\n

4. Car A moves at 72 km\/h and car B moves at 90 km\/h, approach each other. Car A honked with a frequency of 650 Hz. If the speed of the sound waves in air is 350 m\/s, then what is the frequency of sound heard by the driver of car B from car A.<\/span><\/p>\n

Known :<\/u><\/span><\/p>\n

The speed of car A (vA<\/sub>) = 72 km\/h = 20 m\/s, approach car B<\/span><\/p>\n

The speed of car B (vB<\/sub>) = 90 km\/h = 25 m\/s, approach car A<\/span><\/p>\n

The frequency of the sound of car A (fA<\/sub>) = 650 Hz <\/span><\/p>\n

The speed of the sound waves in air (v) = 350 m\/s<\/span><\/p>\n

Wanted: Frequency of sound heard by the driver of the car B from car A<\/span><\/p>\n

Solution :<\/u><\/span><\/p>\n

The sound speed (v) always positive<\/span><\/p>\n

The observer speed (vobs<\/sub>) is positive if observer moving toward the source of the sound<\/span><\/p>\n

The observer speed (vobs<\/sub>) is negative if the observer moving away from the source of the sound<\/span><\/p>\n

The source speed (vsource<\/sub>) is positive if the source of the sound moving away from the observer<\/span><\/p>\n

The source speed (vsource<\/sub>) is negative if the source <\/span>of the sound moving toward the observer<\/span><\/p>\n

The observer speed (vobs<\/sub>) = 0 if an observer at rest<\/span><\/p>\n

The source speed (vsource<\/sub>) = 0 if source at rest<\/span><\/p>\n

\"Doppler<\/span><\/p>\n

5. A source of sound moves at 10 m\/s approach a stationary observer. The frequency of the source of the sound is 380 Hz and the speed of the sound waves in air is 400 m\/s What is the frequency of the sound waves heard by the observer.<\/span><\/p>\n

Known :<\/u><\/span><\/p>\n

The speed of the source of the sound (vs<\/sub>) = 20 m\/s<\/span><\/p>\n

The speed of observer (vp<\/sub>) = 0<\/span><\/p>\n

The frequency of the source of the sound (f) = 380 Hz<\/span><\/p>\n

The speed of the sound waves in air (v) = 400 m\/s<\/span><\/p>\n

Wanted:<\/u> The frequency of the sound waves heard by the observer<\/span><\/p>\n

Solution :<\/u><\/span><\/p>\n

The sound speed (v) always positive<\/span><\/p>\n

The observer speed (vobs<\/sub>) is positive if observer moving toward the source of the sound<\/span><\/p>\n

The observer speed (vobs<\/sub>) is negative if the observer moving away from the source of the sound<\/span><\/p>\n

The source speed (vsource<\/sub>) is positive if the source of the sound moving away from observer<\/span><\/p>\n

The source speed (vsource<\/sub>) is negative if the source of the sound moving toward the observer<\/span><\/p>\n

The observer speed (vobs<\/sub>) = 0 if an observer at rest<\/span><\/p>\n

The source speed (vsource<\/sub>) = 0 if source at rest<\/span><\/p>\n

\"Doppler<\/span><\/p>\n

6. A car moving toward a stationary observer that emits 490 Hz sound wave. The beat frequency heard is 10 Hz. If the speed of the sound waves in air is 340 m\/s, what is the speed of the car?<\/span><\/p>\n

Known :<\/u><\/span><\/p>\n

The frequency of sound (f) = 490 Hertz<\/span><\/p>\n

The speed of the sound waves in air (v) = 340 m\/s<\/span><\/p>\n

The <\/span>observer <\/span>approaches the sound source so that <\/span>the frequency of sound heard is <\/span>greater than the frequency of the sound source. The frequency of sound <\/span>= <\/span>490 Hertz and the beat frequency = 10 Hertz so that the frequency of the sound heard by an observer (f’) = 500 Hertz.<\/span><\/p>\n

Wanted:<\/u> the speed of the car<\/span><\/p>\n

Solution :<\/u><\/span><\/p>\n

The equation of the Doppler effect :<\/span><\/p>\n

\"Doppler<\/span><\/p>\n

Sign rule :<\/span><\/p>\n

The sound speed (v) always positive<\/span><\/p>\n

The observer speed (vobs<\/sub>) is positive if observer moving toward the source of the sound<\/span><\/p>\n

The observer speed (vobs<\/sub>) is negative if the observer moving away from the source of the sound<\/span><\/p>\n

The source speed (vsource<\/sub>) is positive if the source of the sound moving away from the observer<\/span><\/p>\n

The source speed (vsource<\/sub>) is negative if the source of the sound moving toward the observer<\/span><\/p>\n

The observer speed (vobs<\/sub>) = 0 if an observer at rest<\/span><\/p>\n

The source speed (vsource<\/sub>) = 0 if source at rest<\/span><\/p>\n

\"Doppler<\/span><\/p>\n

The speed of the car is 6.9 m\/s.<\/span><\/p>\n

7. The police car that was ringing a 930 Hz siren chased after someone who ran away on a motorcycle with a speed of 72 km.jam-1<\/sup>. The speed of police cars reaches 108 km.hour-1<\/sup>. If the speed of sound in the air is 340 m.s-1, then the frequency of siren sounds heard by motorcyclists is …<\/span><\/p>\n

Solution :<\/span><\/p>\n

Sign rule :<\/span><\/p>\n

The sound speed (v) always positive<\/span><\/p>\n

The observer speed (vobs<\/sub>) is positive if observer moving toward the source of the sound<\/span><\/p>\n

The observer speed (vobs<\/sub>) is negative if the observer moving away from the source of the sound<\/span><\/p>\n

The source speed (vsource<\/sub>) is positive if the source of the sound moving away from the observer<\/span><\/p>\n

The source speed (vsource<\/sub>) is negative if the source of the sound moving toward the observer<\/span><\/p>\n

The observer speed (vobs<\/sub>) = 0 if an observer at rest<\/span><\/p>\n

The source speed (vsource<\/sub>) = 0 if source at rest<\/span><\/p>\n

Known :<\/u><\/span><\/p>\n

The frequency of the source of sound (f) = 930 Hz<\/span><\/p>\n

The speed of observer (vp<\/sub>) = 72 km.hour-1<\/sup> = 72 (1000 meters) \/ 3600 (seconds) = 72,000\/3600 meters\/second = 20 m\/s = -20 m.s-1<\/sup><\/span><\/p>\n

The speed of the source of sound (vsource<\/sub>) = 108 km.hour-1 <\/sup>= 108 (1000 meters) \/ (3600 seconds) = 108,000 \/ 3600 meters\/second = 30 m\/s = -30 m.s-1<\/sup><\/span><\/p>\n

The speed of the source of the sound waves (v) = 340 m.s-1<\/sup><\/span><\/p>\n

Wanted :<\/u> The frequency of the sound waves heard by an observer (f\u2019)<\/span><\/p>\n

Solution :<\/u><\/span><\/p>\n

The equation of the Doppler effect :<\/span><\/p>\n

\"Doppler<\/span><\/p>\n

8. An ambulance moves at 72 km.hour-1<\/sup> while sounding a siren with a frequency of 1500 Hz. Motorcyclists move at speeds of 20 m.s-1<\/sup> in opposite directions with ambulances. If the speed of sound in air is 340 m.s-1<\/sup>, then the ratio of frequencies heard by motorcyclists when approaching and away from the ambulance is …<\/span><\/p>\n

Known :<\/u><\/span><\/p>\n

The frequency of the source of sound (f) = 1500 Hz<\/span><\/p>\n

The speed of observer (vp<\/sub>) = 20 m\/s<\/span><\/p>\n

The speed of the source of sound (vsource<\/sub>) = 72 km\/hour = 72 (1000 meters) \/ 3600 seconds = 72,000\/3600 meters\/seconds = 20 m\/s<\/span><\/p>\n

The speed of the source of the sound waves (v) = 340 m\/s<\/span><\/p>\n

Wanted:<\/u> The ratio of frequencies heard by motorcyclists when approaching and away from the ambulance<\/span><\/p>\n

Solution :<\/u><\/span><\/p>\n

The equation of the Doppler effect :<\/span><\/p>\n

\"Doppler<\/span><\/p>\n

Frequencies heard by motorcyclists approaching ambulances<\/b><\/span><\/p>\n

Both are in opposite directions so that when the motorcycle approaches the ambulance car, the two approach each other. v<\/i><\/span>p <\/i><\/span><\/sub>is positive if the listener approaches the sound source and v<\/i><\/span>s <\/i><\/span><\/sub>is <\/i><\/span>negative if the sound source approaches the listener.<\/i><\/span><\/span><\/p>\n

\"Doppler<\/span><\/p>\n

Frequencies are heard by motorcyclists as they move away from the ambulance<\/span><\/b><\/span><\/p>\n

Both are opposite direction so that when the motorcycle away from the ambulance, both of them away from each other. v<\/span>p <\/span><\/sub>is negative if the listener is away from the sound source and v<\/span>s<\/span><\/sub> is <\/span>positive if the sound source is away from the listener.<\/span><\/i><\/span><\/p>\n

\"Doppler<\/span><\/p>\n

T<\/b>he ratio of frequencies heard by motorcyclists when approaching and away from the ambulance<\/b><\/span><\/p>\n

\"Doppler<\/span><\/p>\n

\n

    \n
  1. What is the Doppler effect?<\/strong><\/span>\n