Answer:
v_s = 66.09 m/s
Explanation:
given,
Varying frequency of the siren = 588 Hz to 398 Hz
speed of sound = 343 m/s
speed of truck calculation
using equation of Doppler's
When the truck is approaching
[tex]f_s = f_0(\dfrac{v-v_s}{v})[/tex]......(1)
Doppler's equation when truck is moving away
[tex]f_s = f_1(\dfrac{v+v_s}{v})[/tex]...........(2)
equating both the equation
[tex] f_0(\dfrac{v-v_s}{v}) = f_1(\dfrac{v+v_s}{v})[/tex]
on simplifying the above equation we get
[tex]v_s = v \dfrac{f_0-f_1}{f_0 + f_1}[/tex]
f_0 = 588 Hz
f_1 = 398
now,
[tex]v_s = 343\times \dfrac{588 -398}{588+ 398}[/tex]
v_s = 66.09 m/s
speed of the truck is equal to v_s = 66.09 m/s
