Lesson The Doppler Shift

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The Doppler Shift

Problem 1

While driving a car, Al honks the horn every 5 seconds. Bill is standing by the side of the road and hears the honks
of the oncoming car every 4.6 seconds. The speed of sound is 330 meters per second. Calculate the speed of Al's car.

Solution


         car, t1         car, t2                   Bill
------------o---------------o-----------------------o--------------
            ---->


The figure shows the situation.
The car moves along the straight road from the left to the right towards Bill.

At the time moment t = t1, when the distance from the car to Bill is D1, the car releases the honk.
After 5 seconds, at the t = t2 = t1+5, when the distance from the car to Bill is D2, the car releases the next honk.

The first honk arrives to the Bill location at the time moment t = .

The next honk arrives to the Bill location at the time moment t = .

The time difference between two successive honks arriving to Bill location is 


 -  =  +  = 5 + .


Also,  D1 - D2 = 5*v,  where v is the car speed.

So, you have this equation

5 -  = 4.6,   or   = 0.4.

Hence,  v =  = 26.4 m/s.


Answer.  The speed of the car is 26.4 m/s  or  95.04 km/h.

My other lessons on Travel and Distance problems in this site are

- Travel and Distance problems
- Travel and Distance problems for two bodies moving in opposite directions
- Travel and Distance problems for two bodies moving in the same direction (catching up)
- Using fractions to solve Travel problems

- Wind and Current problems
- More problems on upstream and downstream round trips
- Wind and Current problems solvable by quadratic equations
- Unpowered raft floating downstream along a river
- Selected problems from the archive on the boat floating Upstream and Downstream
- Selected problems from the archive on a plane flying with and against the wind

- Selected Travel and Distance problems from the archive

- Had a car move faster it would arrive sooner
- How far do you live from school?

- One unusual Travel problem
- Another unusual Travel problem (Arnold's problem on two walking old women)

- Travel problem on a messenger moving back and forth along the marching army's column
- A person walking along the street and buses traveling in the same and opposite directions

    - Calculating an average speed: a train going from A to B and back
    - One more problem on calculating an average speed

    - Clock problems
    - Advanced clock problems
    - Problems on bodies moving on a circle

    - A train passing a telegraph post and passing a bridge
    - A train passing a platform
    - A train passing through a tunnel
    - A light-rail train passing a walking person
    - A train passing another train

    - A man crossing a bridge and a train coming from behind
    - A rower going on a river who missed the bottle of whiskey under a bridge
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    - Entertainment Travel and Distance problems

    - OVERVIEW of lessons on Travel and Distance

Use this file/link ALGEBRA-I - YOUR ONLINE TEXTBOOK to navigate over all topics and lessons of the online textbook ALGEBRA-I.

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