Answer:
The velocity of the truck is [tex]v_2 = 38 \ m/s [/tex]
The velocity of the car is [tex] v_1 = 23 \ m/s [/tex]
Explanation:
From the question we are told that
The natural frequency of a truck horn is [tex]f_t = 800 \ Hz[/tex]
The apparent frequency of the truck horn is [tex]f_h = 960 \ Hz[/tex]
The relative speed is [tex]v_r = 61 \ m/s[/tex]
Generally the relative speed when the truck and the car are moving towards each other is
[tex]v_r = v_1 + v_2[/tex]
Here [tex]v_2 \ and \ v_1[/tex] are the velocities of the truck and the car respectively
[tex]61 = v_1 + v_2[/tex]
=> [tex]v_2 = 61 - v_1[/tex]
Generally the apparent frequency is mathematically represented as
[tex]f_h = \frac{ v - v_1 }{v - v_2} f_t[/tex]
Here v is the speed of sound with value [tex]v = 343 \ m/s[/tex]
=> [tex] \frac{f_h}{f_t} = \frac{ 343 - v_1 }{343 - (61 - v_1)}[/tex]
=> [tex] \frac{960}{800} = \frac{ 343 - v_1 }{ 279 + v_1)}[/tex]
=> [tex] v_1 = 23 \ m/s [/tex]
From the above equation we have that
=> [tex]v_2 = 61 - 23[/tex]
=> [tex]v_2 = 38 \ m/s [/tex]
