Calculate the frequency of the siren

[BioMechanical]

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

 

[Oberst Villa]

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

 

[Moetasim]

Hello,

To calculate the frequency of the siren, we can use the formula:

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

Where:
f = frequency of the siren
V = speed of sound in air (343 m/s)
Vs = speed of the source (34 m/s)
Vd = speed of the detector (15 m/s)
f1 = original frequency of the siren (unknown)

(a) To find f1, we can rearrange the formula to solve for f1:

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

Plugging in the given values, we get:

f1 = (343-15)/(343-34) x 4.80 Hz
f1 = 328/309 x 4.80 Hz
f1 = 5.080 Hz

Therefore, the frequency of the siren is 5.080 Hz.

(b) To calculate the beat frequency heard by the policeman in the second police car, we can use the formula:

fb = |f2-f1|

Where:
fb = beat frequency
f2 = frequency heard by the second policeman (unknown)
f1 = frequency of the siren (5.080 Hz)

We can rearrange the formula to solve for f2:

f2 = fb + f1

Plugging in the given values, we get:

f2 = 4.80 Hz + 5.080 Hz
f2 = 9.880 Hz

Therefore, the beat frequency heard by the second policeman is 9.880 Hz.

(c) To find the frequency from the siren of the faster police car heard by a person standing on the sidewalk between the two cars, we can use the formula:

f = (V+Vd)/(V+Vs) x f1

Where:
f = frequency of the siren
V = speed of sound in air (343 m/s)
Vs = speed of the source (32 m/s)
Vd = speed of the detector (15 m/s)
f1 = original frequency of the siren (unknown)

Plugging in the given values, we get:

f = (343+15)/(343+32) x 5.080 Hz
f = 358/375 x 5.080 Hz
f = 4.846 Hz

Therefore, the frequency from the siren of the faster police car heard by a person standing