Calculate the frequency of the siren

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SUMMARY

The discussion focuses on calculating the frequency of sirens from two police cars moving towards the east, with one car traveling at 34.0 m/s and the other at 32.0 m/s, while a wind from the west blows at 15.0 m/s. The speed of sound in air is given as 343 m/s. The calculated frequency of the siren is 864.0 Hz, the beat frequency heard by the second policeman is 5.333 Hz, and the frequency of the faster police car's siren heard by a person on the sidewalk is 954.7 Hz. The calculations utilize the Doppler effect formula, specifically f1=f(V-Vd/V-Vs).

PREREQUISITES
  • Understanding of the Doppler effect and its application in sound frequency calculations.
  • Familiarity with basic physics concepts such as relative velocity and sound propagation.
  • Knowledge of the formula f1=f(V-Vd/V-Vs) for calculating observed frequencies.
  • Ability to perform calculations involving speed, frequency, and beat frequency.
NEXT STEPS
  • Study the Doppler effect in detail, focusing on sound waves and moving sources.
  • Learn about relative velocity in different reference frames, particularly in the context of wind effects.
  • Explore beat frequency phenomena and its applications in acoustics.
  • Practice similar problems involving multiple moving sound sources and environmental factors.
USEFUL FOR

Students in physics, particularly those studying wave mechanics and sound, as well as educators seeking to explain the Doppler effect and its implications in real-world scenarios.

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Homework Statement



A police car is moving towards the east at 34.0 m/s while sounding its siren. There is a wind blowing from the west with a speed of 15.0 m/s. A second police car is ahead of the first police car and is sounding its identical siren while moving towards the east at 32.0 m/s. A policeman in the first police car hears a beat frequency of 4.80 Hz between the two sirens. The speed of sound in air is 343. m/s.
Calculate
(a) the frequency of the siren;
(b) the beat frequency heard by the policeman in the second police car;
(c) the frequency from the siren of the faster police car heard by a person standing on the sidewalk between the two cars.

Answers
(a) 864.0 Hz
(b) 5.333 Hz
(c) 954.7 Hz

Homework Equations



f1=f(V-Vd/V-Vs)

The Attempt at a Solution



i think v=343-15
v=328m/s
Besides the above, I'm Clueless. Can someone help me out? (no solutions please)
Thanks guys
 
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BioMechanical said:

Homework Statement



A police car is moving towards the east at 34.0 m/s while sounding its siren. There is a wind blowing from the west with a speed of 15.0 m/s. A second police car is ahead of the first police car and is sounding its identical siren while moving towards the east at 32.0 m/s. A policeman in the first police car hears a beat frequency of 4.80 Hz between the two sirens. The speed of sound in air is 343. m/s.
Calculate
(a) the frequency of the siren;
(b) the beat frequency heard by the policeman in the second police car;
(c) the frequency from the siren of the faster police car heard by a person standing on the sidewalk between the two cars.


my first step would be the transformation into a reference frame that is moving with the same velocity as the wind. thereby you take care of the wind once and don't have to consider it during the further calculations. so the transformed velocities of the objects are:

first police car: 19 m/s
second police car: 17 m/s
person: -15 m/s
 

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