Answer:
The velocity of the truck is [tex]v_2 = Â 38 \ m/s [/tex] Â
The velocity of the car is  [tex]  v_1 =  23 \  m/s [/tex] Â
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 \ Â v_1[/tex] are the velocities of the truck and the car respectively
  [tex]61 =  v_1  +  v_2[/tex]
=> Â [tex]v_2 = Â 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]
=> Â Â Â [tex] \frac{f_h}{f_t} Â = Â \frac{ 343 Â - Â v_1 }{343 Â - (61 - v_1)}[/tex]
=> Â Â Â [tex] \frac{960}{800} Â = Â \frac{ 343 Â - Â v_1 }{ 279 + v_1)}[/tex]
=> Â Â [tex] Â v_1 = Â 23 \ Â m/s [/tex]
From the above equation we have that
=> Â [tex]v_2 = Â 61 - 23[/tex] Â Â
=> Â [tex]v_2 = Â 38 \ m/s [/tex] Â Â Â Â
