The Doppler Effect

1. The Doppler Effect
By Brigette Wee

2. The Doppler Effect
What is it?
 It is the shift in frequency of a wave due to the relative motion of the
source of the sound with respect to the receiver of the sound
 If there is relative motion between the source and receiver of sound,
the frequency at the receiver is different from frequency that is
transmitted
 if moving towards each other: received frequency is higher
if moving away from each other: received frequency is lower
 It can be expressed as a single equation:
fr: frequency of the receiver
fs: frequency of source
vr:: speed of receiver
Vs: speed of source
V: speed of wave

3. How do we use the equation?
When do we use ± in the
numerator?
 If the receiver is moving toward
the source, the received frequency
is higher
 Thus, we use the top sign in the
numerator, which is +
 If the receiver is moving away from
the source, the received frequency
is smaller
 Thus, we use the bottom sign in
the numerator, which is -
When do we use
in the denominator?
 If the source is moving toward
the receiver, the received
frequency is higher
Thus, we use the top sign in the
denominator, which is –
 If the source is moving away
from the receiver, the received
frequency is smaller
Thus, we use the bottom sign in
the denominator, which is +

4. Scenario 1:
Moving Source, Stationary Receiver
 Stationary receiver means vr:= 0
 Thus, we use this equation if the source is
moving towards a stationary receiver:
 Note: if the source is moving away from the stationary receiver, a
plus sign would be on the denominator of the equation above
 If source is moving to right, the wave front to the right of source are
closer (as shown in the figure)
meaning there are more waves per second (higher frequency)
thus, the receiver to the right will detect more waves
Note: same rational as above if the source is moving to
the left

5. Scenario 2:
Moving Receiver, Stationary Source
 Stationary source means Vs= 0
 Thus we this equation if the
receiver is moving towards the source:
• Note: if the receiver is moving away from
the source, there would be a – sign on the numerator

6. Scenario 3:
Moving Receiver, Moving Source
 In this case, we can also use the equation:
 The signs on the denominator and numerator will depend on
whether the receiver and source are moving towards or away from
each other
 Please refer to slide 3 for reference.

7. Scenario : A female whale (travelling at
15km/hr) and a male whale (travelling at
25km/hr) are trying to move towards each
other in order to mate. However, they must
first send out sound waves to locate each
other. The male whale sends out a sound
wave travelling at 6000km/hr and a
frequency of 1000Hz
Application of the Doppler Effect
in Whale Mating

8. 25 km/hr
15km/hr


9.  What is the frequency detected by the female whale?
Question 1

10.  First make an educated guess as to whether the
received frequency has a higher/lower magnitude
 Since they are moving towards each other, the
received frequency will be higher
Solution: Step 1

11.  First determine what equation is appropriate in the given
scenario:
They are moving towards each other
They are both moving
So we use this equation:
*Since they are moving towards each other:
*Note the signs
Use a + in the numerator
Use a – in the denominator
REMEMBER: FIGURING OUT THE SIGN IS AN IMPORTANT
STEP (PLEASE REFER TO SLIDE 3 FOR A SUMMARY)
Solution: step 2

12.  Assign the variables:
fr: frequency of female whale (solve for this)
fs: frequency of male whale (1000Hz)
vr:: speed of female whale (15km/hr)
vs: speed of male whale (25km/hr)
v: speed of sound (6000km/hr)
Solution: step 3

13.  Plug in your numbers and you should get…
 Note that km/hr does not need to be converted to m/s as it
cancels out in the fraction.
Solution: Final answer

14.  YESS!! The received frequency
(10006Hz) is higher than 1000Hz
Does our final answer agree with our
educated guess in step 1?

15. THANK YOU

16.  Physics for Scientist and Engineers An Interactive
Approach by Hawkes, Iqbal, Mansour Milner-Bolotin,
Williams
Work cited