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The natural frequency of a truck horn is 800 Hz. The driver of a car perceives the horn to be960 Hz. Given that both the truck and car are moving and have a relative speed of 61 m/s, whatare their individual speeds

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Answer:

The velocity of the truck is
v_2 =  38 \ m/s

The velocity of the car is
v_1 =  23 \  m/s

Step-by-step explanation:

From the question we are told that

The natural frequency of a truck horn is
f_t  =  800 \  Hz

The apparent frequency of the truck horn is
f_h  =  960 \  Hz

The relative speed is
v_r  =  61 \  m/s

Generally the relative speed when the truck and the car are moving towards each other is


v_r  =  v_1  +  v_2

Here
v_2 \ and \  v_1 are the velocities of the truck and the car respectively


61 =  v_1  +  v_2

=>
v_2 =  61 - v_1

Generally the apparent frequency is mathematically represented as


f_h  =  ( v  -  v_1 )/(v - v_2) f_t

Here v is the speed of sound with value
v  =  343 \  m/s

=>
(f_h)/(f_t)  =  ( 343   -  v_1 )/(343  - (61 - v_1))

=>
(960)/(800)  =  ( 343   -  v_1 )/( 279 + v_1))

=>
v_1 =  23 \  m/s

From the above equation we have that

=>
v_2 =  61 - 23

=>
v_2 =  38 \ m/s

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