Printable worksheet

← Back to the Doppler Effect Calculator

In the print window, choose “Save as PDF” as the printer (or print it on paper). Seed 1 rebuilds this exact sheet.

Doppler Effect worksheet

Grades 11–12

Solve each problem and show your work. Round answers to 2 decimal places where needed.

1.
Problem 1.
- Sign convention for the speeds: Positive = the direction pointing from source to observer
- Emitted frequency (f): 450 Hz
- Wave speed in the medium (v): 360 m/s
- Source velocity (vₛ): 35 m/s
- Observer velocity (vₒ): 0 m/s
Find: Observed frequency (f′)
Answer
2.
Problem 2.
- Sign convention for the speeds: Positive = moving toward the other
- Emitted frequency (f): 350 Hz
- Wave speed in the medium (v): 340 m/s
- Source velocity (vₛ): 26 m/s
- Observer velocity (vₒ): 0 m/s
Find: Observed frequency (f′)
Answer
3.
Problem 3.
- Sign convention for the speeds: Positive = moving toward the other
- Emitted frequency (f): 450 Hz
- Wave speed in the medium (v): 325 m/s
- Source velocity (vₛ): 36 m/s
- Observer velocity (vₒ): 0 m/s
Find: Observed frequency (f′)
Answer
4.
Problem 4.
- Sign convention for the speeds: Positive = moving toward the other
- Emitted frequency (f): 350 Hz
- Wave speed in the medium (v): 280 m/s
- Source velocity (vₛ): 32 m/s
- Observer velocity (vₒ): 0 m/s
Find: Observed frequency (f′)
Answer
5.
Problem 5.
- Sign convention for the speeds: Positive = the direction pointing from source to observer
- Emitted frequency (f): 400 Hz
- Wave speed in the medium (v): 500 m/s
- Source velocity (vₛ): 26 m/s
- Observer velocity (vₒ): 0 m/s
Find: Observed frequency (f′)
Answer
6.
Problem 6.
- Sign convention for the speeds: Positive = moving toward the other
- Emitted frequency (f): 600 Hz
- Wave speed in the medium (v): 380 m/s
- Source velocity (vₛ): 30 m/s
- Observer velocity (vₒ): 0 m/s
Find: Observed frequency (f′)
Answer
7.
Problem 7.
- Sign convention for the speeds: Positive = moving toward the other
- Emitted frequency (f): 450 Hz
- Wave speed in the medium (v): 380 m/s
- Source velocity (vₛ): 28 m/s
- Observer velocity (vₒ): 0 m/s
Find: Observed frequency (f′)
Answer
8.
Problem 8.
- Sign convention for the speeds: Positive = moving toward the other
- Emitted frequency (f): 440 Hz
- Wave speed in the medium (v): 225 m/s
- Source velocity (vₛ): 28 m/s
- Observer velocity (vₒ): 0 m/s
Find: Observed frequency (f′)
Answer
9.
Problem 9.
- Sign convention for the speeds: Positive = moving toward the other
- Emitted frequency (f): 550 Hz
- Wave speed in the medium (v): 290 m/s
- Source velocity (vₛ): 36 m/s
- Observer velocity (vₒ): 0 m/s
Find: Observed frequency (f′)
Answer
10.
Problem 10.
- Sign convention for the speeds: Positive = moving toward the other
- Emitted frequency (f): 500 Hz
- Wave speed in the medium (v): 220 m/s
- Source velocity (vₛ): 32 m/s
- Observer velocity (vₒ): 0 m/s
Find: Observed frequency (f′)
Answer

Answer key: Doppler Effect worksheet

1. Observed frequency (f′): 498.46 Hz
1. Use the Doppler formula. Moving closer packs the waves tighter, so the pitch you hear goes up
  $450 \times \frac{360 + 0}{360 - 35}$ $= 450 \times \frac{360}{325}$ $= 498.461538 Hz$
2. Take away the starting tone to see how far the pitch moved
  $498.461538 - 450$ $= 48.461538 Hz$
2. Observed frequency (f′): 378.98 Hz
1. Use the Doppler formula. Moving closer packs the waves tighter, so the pitch you hear goes up
  $350 \times \frac{340 + 0}{340 - 26}$ $= 350 \times \frac{340}{314}$ $= 378.980892 Hz$
2. Take away the starting tone to see how far the pitch moved
  $378.980892 - 350$ $= 28.980892 Hz$
3. Observed frequency (f′): 506.06 Hz
1. Use the Doppler formula. Moving closer packs the waves tighter, so the pitch you hear goes up
  $450 \times \frac{325 + 0}{325 - 36}$ $= 450 \times \frac{325}{289}$ $= 506.055363 Hz$
2. Take away the starting tone to see how far the pitch moved
  $506.055363 - 450$ $= 56.055363 Hz$
4. Observed frequency (f′): 395.16 Hz
1. Use the Doppler formula. Moving closer packs the waves tighter, so the pitch you hear goes up
  $350 \times \frac{280 + 0}{280 - 32}$ $= 350 \times \frac{280}{248}$ $= 395.16129 Hz$
2. Take away the starting tone to see how far the pitch moved
  $395.16129 - 350$ $= 45.16129 Hz$
5. Observed frequency (f′): 421.94 Hz
1. Use the Doppler formula. Moving closer packs the waves tighter, so the pitch you hear goes up
  $400 \times \frac{500 + 0}{500 - 26}$ $= 400 \times \frac{500}{474}$ $= 421.940928 Hz$
2. Take away the starting tone to see how far the pitch moved
  $421.940928 - 400$ $= 21.940928 Hz$
6. Observed frequency (f′): 651.43 Hz
1. Use the Doppler formula. Moving closer packs the waves tighter, so the pitch you hear goes up
  $600 \times \frac{380 + 0}{380 - 30}$ $= 600 \times \frac{380}{350}$ $= 651.428571 Hz$
2. Take away the starting tone to see how far the pitch moved
  $651.428571 - 600$ $= 51.428571 Hz$
7. Observed frequency (f′): 485.8 Hz
1. Use the Doppler formula. Moving closer packs the waves tighter, so the pitch you hear goes up
  $450 \times \frac{380 + 0}{380 - 28}$ $= 450 \times \frac{380}{352}$ $= 485.795455 Hz$
2. Take away the starting tone to see how far the pitch moved
  $485.795455 - 450$ $= 35.795455 Hz$
8. Observed frequency (f′): 502.54 Hz
1. Use the Doppler formula. Moving closer packs the waves tighter, so the pitch you hear goes up
  $440 \times \frac{225 + 0}{225 - 28}$ $= 440 \times \frac{225}{197}$ $= 502.538071 Hz$
2. Take away the starting tone to see how far the pitch moved
  $502.538071 - 440$ $= 62.538071 Hz$
9. Observed frequency (f′): 627.95 Hz
1. Use the Doppler formula. Moving closer packs the waves tighter, so the pitch you hear goes up
  $550 \times \frac{290 + 0}{290 - 36}$ $= 550 \times \frac{290}{254}$ $= 627.952756 Hz$
2. Take away the starting tone to see how far the pitch moved
  $627.952756 - 550$ $= 77.952756 Hz$
10. Observed frequency (f′): 585.11 Hz
1. Use the Doppler formula. Moving closer packs the waves tighter, so the pitch you hear goes up
  $500 \times \frac{220 + 0}{220 - 32}$ $= 500 \times \frac{220}{188}$ $= 585.106383 Hz$
2. Take away the starting tone to see how far the pitch moved
  $585.106383 - 500$ $= 85.106383 Hz$