How Do You Calculate Motorcycle Speed Using the Doppler Effect?

In summary, the problem involves two motorcycles traveling at the speed of sound in opposite directions. One cyclist blasts her horn at a frequency of 544 Hz, which the other cyclist hears as 563 Hz. To solve for the speed of the motorcycles, the equation f[o] = f[s] * ( ( v + v[o] ) / ( v – v[s] ) ) is used, and by setting v[s] = v[o], the speed of the motorcycles can be calculated to be 5.88 m/s.
  • #1
dustybray
10
0
I'm having trouble solving this one:

Two motorcycles are traveling in opposite directions at the same speed, when one of the cyclists blasts her horn, which has a frequency of 544 Hz. The other cyclist hears the frequency as 563 Hz. If the speed of sound in air is 344 m/s, what is the speed of the motorcycles? Ans. 5.88 m/s

If I use f[o] = f * ( ( v + v[o] ) / ( v – v ) )

Then I guess I could make v = -v[o]; so,
( f[o] / f ) = ( ( v + v[o] ) / ( v + v[o] ) )
or
( f[o] / f ) = ( ( v - v[o] ) / ( v - v[o] ) )

But how do I solve for v[o]??

Thanks,

dusty...
 
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  • #2
Starting with f[o] = f * ( ( v + v[o] ) / ( v – v ) ),

then f[o]/f = ( ( v + v[o] ) / ( v – v ) ), and then

f[o]/f * ( v – v ) = ( ( v + v[o] ), and then let v = v[o].

But one may be confusing v's.

The equation should include the speed of sound, and in the initial equation, v would be the speed of sound, and on then solves for v,v[o], both being equal.
 
  • #3


I would suggest breaking down the problem into smaller steps and using equations that relate to the Doppler effect. First, let's define the variables:

f[o] = original frequency of the horn (544 Hz)
f = frequency heard by the other cyclist (563 Hz)
v = speed of sound in air (344 m/s)
v[o] = speed of the motorcycle that is honking the horn
v = speed of the other motorcycle

Next, we can use the equation for the Doppler effect to relate the frequencies and speeds:

f = f[o] * ( ( v + v ) / ( v + v[o] ) )

Now, we can substitute in the known values and solve for v[o]:

563 Hz = 544 Hz * ( ( 344 m/s + v ) / ( 344 m/s + v[o] ) )

Rearranging the equation, we get:

( 563 Hz * ( 344 m/s + v[o] ) ) / 544 Hz = ( 344 m/s + v )

Multiplying both sides by 544 Hz, we get:

563 Hz * ( 344 m/s + v[o] ) = 544 Hz * ( 344 m/s + v )

Expanding the brackets, we get:

193472 Hz + 563 Hz * v[o] = 187136 Hz + 544 Hz * v

Subtracting 193472 Hz from both sides and rearranging, we get:

563 Hz * v[o] = 544 Hz * v - 193472 Hz

Dividing both sides by 563 Hz, we get:

v[o] = ( 544 Hz * v - 193472 Hz ) / 563 Hz

Now, we can plug in the known values for v and solve for v[o]:

v[o] = ( 544 Hz * 5.88 m/s - 193472 Hz ) / 563 Hz

Simplifying, we get:

v[o] = ( 3203.52 m/s - 193472 Hz ) / 563 Hz

Dividing by 563 Hz, we get:

v[o] = 5.88 m/s

Therefore, the speed of the motorcycle that is honking the horn is 5.88 m/s. I hope this helps you solve the problem. Remember to always define
 

Related to How Do You Calculate Motorcycle Speed Using the Doppler Effect?

1. What is the Doppler effect?

The Doppler effect is a phenomenon in physics where the frequency and wavelength of a wave appear to change when the source of the wave is moving relative to the observer.

2. How does the Doppler effect affect sound waves?

When a sound source is moving towards an observer, the frequency of the sound waves will appear higher, resulting in a higher pitch. Conversely, when the sound source is moving away from the observer, the frequency will appear lower, resulting in a lower pitch.

3. How is the Doppler effect used in real-life situations?

The Doppler effect is used in various real-life situations, such as in radar technology used in air traffic control and weather forecasting, in medical ultrasound imaging, and in astronomy to determine the relative motion of stars and galaxies.

4. What is the difference between the Doppler effect for sound waves and light waves?

The Doppler effect for sound waves is based on changes in the frequency and pitch of the wave, while the Doppler effect for light waves is based on changes in the wavelength and color of the wave.

5. How is Doppler physics homework typically solved?

Doppler physics homework is typically solved using the Doppler equation, which relates the frequency or wavelength of a wave to the relative velocity between the source and observer. Students may also be required to use graphical representations or mathematical calculations to solve problems related to the Doppler effect.

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