An ice cream truck is making its way down the street and two children hear it an

Question

An ice cream truck is making its way down the street and two children hear it and begin running. Child 1 is in front of the truck running towards it with a speed 4.00m/s and hears a frequency of 449Hz. Child 2 is lactose intolerant and runs away from the truck with a speed of 8.00m/s and hears a frequency of 426Hz.
What is the speed and frequency of the source? An ice cream truck is making its way down the street and two children hear it and begin running. Child 1 is in front of the truck running towards it with a speed 4.00m/s and hears a frequency of 449Hz. Child 2 is lactose intolerant and runs away from the truck with a speed of 8.00m/s and hears a frequency of 426Hz.
What is the speed and frequency of the source?
What is the speed and frequency of the source?

Explanation / Answer

Speed of child 1 is v ' = 4m/s

Apperent frequency f ' = 449 Hz

Speed of the sound V = 340 m/s

We know f ' = [(V+v ')/(V-v )]f

            449 = [(340+4) /(340-v ) ] f

             449 = [344/(340-v)]f          ------------( 1)

Speed of child 2 is v " = 8 m/s

Apperent frequency f " = 426 Hz

We know f ' = [(V-v ')/(V-v )]f

            426 = [(340-8) /(340+v ) ] f

                  = [336/(340+v)] f         ------------( 2)

Equation( 1) / equation( 2) ==>

449 / 426 = [344/(340-v)][(340+v)/336]

              = (344/336)(340-v)/(340+v)

(449x336)/(426x344) = (340-v)/(340+v)

1.02947 = (340-v) /(340+v)

1.02947 (340+v) = 340-v

350 +1.02947 v = 340 -v

          2.02947 v = -10

                      v = -4.927 m/s

So, speed of the source v = 4.927 m/s

Substitute this in equation( 1) you get ,

449 = [344/(340-4.927)]f

       = 1.0266 f

from this freuqnecy of the source f = 449 / 1.0266

                                                  = 437.34 Hz

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.