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the doppler effect by Brigette Wee

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the doppler effect by Brigette Wee

  1. 1. The Doppler Effect By Brigette Wee
  2. 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. 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. 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. 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. 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. 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. 8. 25 km/hr 15km/hr 
  9. 9.  What is the frequency detected by the female whale? Question 1
  10. 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. 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. 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. 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. 14.  YESS!! The received frequency (10006Hz) is higher than 1000Hz Does our final answer agree with our educated guess in step 1?
  15. 15. THANK YOU
  16. 16.  Physics for Scientist and Engineers An Interactive Approach by Hawkes, Iqbal, Mansour Milner-Bolotin, Williams Work cited

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