An observer measures a 100 Hz Doppler shift as an ambulance goes by. At rest, the frequency of the ambulance's siren is 2,000 Hz. What is the speed of the ambulance?

8.6 m/s

Explanation:

The observer is stationary

The source is moving

Let v₀ be the speed of sound in the air

Let v be the speed of the ambulance

As the siren approaches

f₁ = 2000(v₀ / (v₀ - v))

As the siren departs

f₁' = 2000(v₀ / (v₀ + v))

                                                                         f₁ - f₁' = 100  

                     2000(v₀ / (v₀ - v)) - 2000(v₀ / (v₀ + v)) = 100

                                           v₀ / (v₀ - v) -  v₀ / (v₀ + v) = 100/2000

v₀(v₀ + v) / (v₀ - v)(v₀ + v) -  v₀(v₀ - v) / (v₀ - v)(v₀ + v) = 0.05

                              (v₀² + vv₀) -  (v₀² - vv₀) / (v₀² - v²) = 0.05

                                                          2vv₀ / (v₀² - v²) = 0.05

                                                                         2vv₀  = 0.05 (v₀² - v²)

                                           0.05v² + 2vv₀ - 0.05v₀² =  0

                                                         v² + 40vv₀ - v₀² = 0

quadratic formula positive answer

v = (-40v₀ + √((40v₀)² - 4(1)(v₀²))) / 2

v = (-40v₀ + √(1604v₀²)) / 2

v = (0.049968v₀) / 2

v = 0.02498439v₀

If we assume the speed of sound in air is 343 m/s

v = 8.56964... = 8.6  m/s

Approaching frequency heard is 2051 Hz

Departing frequency heard is 1951 Hz

step-by-step explanation:

we are given

we have to simplify it

firstly, we will factor it

now, we can cancel like terms

now, we can combine it

so, we get

a.metals can become magnetic if they have many spinning electrons that create magnetic fields.d.only some metals are attracted by magnets; these metals are called ferromagnetic.

d.wrapping an insulated wire around a metal with ferromagnetic properties and applying an electric current.