Question

Two truckers are traveling directly away from each other at the same speed. If one trucker sounds her horn at a frequency of 211 Hz, and the other trucker hears a frequency of 187 Hz, determine the speed of the trucks. Use the speed of sound as 343 m/s.

Answer 1

The speed of the truck is 20.68 m/s.

Step-by-step explanation:

Given that,

Frequency of horn = 211 Hz

Trucker hears a frequency = 187 Hz

Speed of sound = 343 m/s

Let the speed of the truck is
`v_(T)`

We need to calculate the speed of truck

Using Doppler shift

`f = f_(0)(v'-v_(0))/(v'+v_(s))`

Where,
`f_(0)` = horn frequency

f = Trucker hears a frequency

v'=speed of sound

`v_(0)` = speed of observer

v = speed of source

Put the value in to the formula

`187=211*((343+v_(T))/(343+v_(T)))`

`v_(T)=(211*343-187*343)/(398)`

`v_(T)=20.68\ m/s`

Hence, The speed of the truck is 20.68 m/s.