Calculating Speed of Waves, frequency and Velocity worksheet ... - Free Printable

Let's solve each problem step by step using the wave speed formula:

$$
v = f \lambda
$$

Where:
- $ v $ = wave speed (in m/s)
- $ f $ = frequency (in Hz)
- $ \lambda $ = wavelength (in meters)

We can rearrange this formula as needed:
- $ f = \frac{v}{\lambda} $
- $ \lambda = \frac{v}{f} $

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1. A wave has a frequency of 50 hertz and a wavelength of 10 meters. What is the wavespeed?

$$
v = f \lambda = 50 \, \text{Hz} \times 10 \, \text{m} = 500 \, \text{m/s}
$$

✔ Answer: 500 m/s

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2. A wave has a frequency of 5 Hz and a wavespeed of 25 m/s, what is the wavelength?

$$
\lambda = \frac{v}{f} = \frac{25 \, \text{m/s}}{5 \, \text{Hz}} = 5 \, \text{m}
$$

✔ Answer: 5 m

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3. A wave has a wavelength of 10 meters and a wavespeed of 340 m/s, what is the frequency?

$$
f = \frac{v}{\lambda} = \frac{340 \, \text{m/s}}{10 \, \text{m}} = 34 \, \text{Hz}
$$

✔ Answer: 34 Hz

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4. A wave with frequency of 13 Hz and wavelength of 4 meters. At what speed will the wave travel?

$$
v = f \lambda = 13 \, \text{Hz} \times 4 \, \text{m} = 52 \, \text{m/s}
$$

✔ Answer: 52 m/s

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5. A wave is moving 65 m/s, if the wavelength is 1.5 meters, what is the frequency?

$$
f = \frac{v}{\lambda} = \frac{65 \, \text{m/s}}{1.5 \, \text{m}} = 43.33 \, \text{Hz} \approx 43.3 \, \text{Hz}
$$

✔ Answer: ~43.3 Hz

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6. A wave has a frequency of 46 Hz and a wavelength of 2.3 meters. What is the speed of the wave?

$$
v = f \lambda = 46 \, \text{Hz} \times 2.3 \, \text{m} = 105.8 \, \text{m/s}
$$

✔ Answer: 105.8 m/s

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7. A wave with frequency of 500 Hz is traveling at a speed of 100 m/s. What is the wavelength?

$$
\lambda = \frac{v}{f} = \frac{100 \, \text{m/s}}{500 \, \text{Hz}} = 0.2 \, \text{m}
$$

✔ Answer: 0.2 m

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8. A wave has a wavelength of 125 meters and is moving at speed of 20 m/s, what is its frequency?

$$
f = \frac{v}{\lambda} = \frac{20 \, \text{m/s}}{125 \, \text{m}} = 0.16 \, \text{Hz}
$$

✔ Answer: 0.16 Hz

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9. A wave has a wavelength of 80 meters and a frequency of 60 Hz, what is its velocity?

$$
v = f \lambda = 60 \, \text{Hz} \times 80 \, \text{m} = 4800 \, \text{m/s}
$$

✔ Answer: 4800 m/s

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10. A wave has a velocity of 45 m/s and a wavelength of 9 meters. What is the wave’s frequency?

$$
f = \frac{v}{\lambda} = \frac{45 \, \text{m/s}}{9 \, \text{m}} = 5 \, \text{Hz}
$$

✔ Answer: 5 Hz

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11. A wave is moving at 300 m/s and has a frequency of 25 Hz, what is the wavelength?

$$
\lambda = \frac{v}{f} = \frac{300 \, \text{m/s}}{25 \, \text{Hz}} = 12 \, \text{m}
$$

✔ Answer: 12 m

---

12. A wave has a frequency of 53 Hz and a wavelength of 4 meters. What is its wavespeed?

$$
v = f \lambda = 53 \, \text{Hz} \times 4 \, \text{m} = 212 \, \text{m/s}
$$

✔ Answer: 212 m/s

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13. A wave has a velocity of 72 m/s and a frequency of 12 Hz, what is the wavelength?

$$
\lambda = \frac{v}{f} = \frac{72 \, \text{m/s}}{12 \, \text{Hz}} = 6 \, \text{m}
$$

✔ Answer: 6 m

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14. A wave has a wavelength of 87 meters and a frequency of 4 Hz, what is the wavespeed?

$$
v = f \lambda = 4 \, \text{Hz} \times 87 \, \text{m} = 348 \, \text{m/s}
$$

✔ Answer: 348 m/s

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✔ Final Answers Summary:

| Problem | Answer |
|--------|--------|
| 1 | 500 m/s |
| 2 | 5 m |
| 3 | 34 Hz |
| 4 | 52 m/s |
| 5 | ~43.3 Hz |
| 6 | 105.8 m/s |
| 7 | 0.2 m |
| 8 | 0.16 Hz |
| 9 | 4800 m/s |
| 10 | 5 Hz |
| 11 | 12 m |
| 12 | 212 m/s |
| 13 | 6 m |
| 14 | 348 m/s |

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📌 Tip: Use the triangle method shown in the image:
- Cover the variable you want to find.
- If $ v $ is covered, then $ v = f \lambda $
- If $ f $ is covered, then $ f = v / \lambda $
- If $ \lambda $ is covered, then $ \lambda = v / f $

You can now use these answers to color in the picture on the next page! Let me know if you need help with that too.