The speed of the truck will be equal to v = 66.09 m/s
Velocity is defined as the ratio of the distance moved by the object in a particular time. The velocity is a vector quantity so it needs both the magnitude and the direction.
Given that:-
Varying frequency of the siren = 588 Hz to 398 Hz
speed of sound = 343 m/s
speed of truck calculation
using the equation of Doppler's
When the truck is approaching
[tex]f_s=f_o(\dfrac{v-v_s}{v})[/tex]......(1)
Doppler's equation when the truck is moving away
[tex]f_1(\dfrac{v+v_s}{v})[/tex]...........(2)
equating both the equation
[tex]f_o(\dfrac{v-v_s}{v}) =[/tex][tex]f_o(\dfrac{v-v_s}{v})[/tex]
By simplifying the above equation we get
[tex]v_s=v(\dfrac{f_o-f_1}{f_o+f_1})[/tex]
f₀ = 588 Hz
f₁ = 398
Now, the velocity will be
[tex]v_s=343(\dfrac{588-398}{588+398})[/tex]
v = 66.09 m/s
Therefore the speed of the truck is equal to v = 66.09 m/s
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