Calculating Wave Speed, Frequency, and Wavelength Formulas ... - Free Printable

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

Formulas:

- $ v = \lambda \times f $
- $ f = \frac{v}{\lambda} $
- $ \lambda = \frac{v}{f} $

Where:
- $ v $ stands for wave speed (m/s)
- $ \lambda $ stands for wavelength (m)
- $ f $ stands for frequency (Hz)

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1. What is the speed (v) of a wave that has a wavelength (λ) of 2 m and a frequency of 6 Hz?

| Solving for | Equation |
|-------------|----------|
| Speed (v) | $ v = \lambda \times f $ |

| Substitute | Answer w/ units |
|-----------|-----------------|
| $ v = 2 \, \text{m} \times 6 \, \text{Hz} $ | $ v = 12 \, \text{m/s} $ |

✔ Answer: $ \boxed{12 \, \text{m/s}} $

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2. Calculate the speed of a wave with a frequency of 2 Hz, amplitude of 3 m, and a wavelength of 10 m.

> Note: Amplitude is not needed to calculate wave speed.

| Solving for | Equation |
|-------------|----------|
| Speed (v) | $ v = \lambda \times f $ |

| Substitute | Answer w/ units |
|-----------|-----------------|
| $ v = 10 \, \text{m} \times 2 \, \text{Hz} $ | $ v = 20 \, \text{m/s} $ |

✔ Answer: $ \boxed{20 \, \text{m/s}} $

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3. If two wavelengths pass a given point each second, and the distance between wave crests is 3 m, what is the wave speed?

- Frequency $ f = 2 \, \text{Hz} $ (since 2 wavelengths per second)
- Wavelength $ \lambda = 3 \, \text{m} $

| Solving for | Equation |
|-------------|----------|
| Speed (v) | $ v = \lambda \times f $ |

| Substitute | Answer w/ units |
|-----------|-----------------|
| $ v = 3 \, \text{m} \times 2 \, \text{Hz} $ | $ v = 6 \, \text{m/s} $ |

✔ Answer: $ \boxed{6 \, \text{m/s}} $

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4. The lowest pitch that the average human can hear has a frequency of 20 Hz. If sound with this frequency has a wave speed of 340 m/s, what is its wavelength?

| Solving for | Equation |
|-------------|----------|
| Wavelength ($ \lambda $) | $ \lambda = \frac{v}{f} $ |

| Substitute | Answer w/ units |
|-----------|-----------------|
| $ \lambda = \frac{340 \, \text{m/s}}{20 \, \text{Hz}} $ | $ \lambda = 17 \, \text{m} $ |

✔ Answer: $ \boxed{17 \, \text{m}} $

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5. A bottlenose dolphin can hear sounds with frequencies up to 150,000 Hz. If the speed of sound in sea water is approximately 1,500 m/s, what is the wavelength?

| Solving for | Equation |
|-------------|----------|
| Wavelength ($ \lambda $) | $ \lambda = \frac{v}{f} $ |

| Substitute | Answer w/ units |
|-----------|-----------------|
| $ \lambda = \frac{1500 \, \text{m/s}}{150,000 \, \text{Hz}} $ | $ \lambda = 0.01 \, \text{m} $ or $ 1 \, \text{cm} $ |

✔ Answer: $ \boxed{0.01 \, \text{m}} $ or $ \boxed{1 \, \text{cm}} $

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6. Waves in the ocean are 6 m apart and pass a surfer every 2 s. What is the wave speed?

- Wavelength $ \lambda = 6 \, \text{m} $
- Time between waves = 2 s → So frequency $ f = \frac{1}{2} = 0.5 \, \text{Hz} $

| Solving for | Equation |
|-------------|----------|
| Speed (v) | $ v = \lambda \times f $ |

| Substitute | Answer w/ units |
|-----------|-----------------|
| $ v = 6 \, \text{m} \times 0.5 \, \text{Hz} $ | $ v = 3 \, \text{m/s} $ |

✔ Answer: $ \boxed{3 \, \text{m/s}} $

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✔ Final Answers Summary:

1. $ 12 \, \text{m/s} $
2. $ 20 \, \text{m/s} $
3. $ 6 \, \text{m/s} $
4. $ 17 \, \text{m} $
5. $ 0.01 \, \text{m} $ (or 1 cm)
6. $ 3 \, \text{m/s} $

All problems use the core wave equation $ v = \lambda f $, rearranged as needed. Remember:
- Amplitude does not affect wave speed.
- Frequency is cycles per second (Hz).
- Wavelength is distance between crests (m).

Let me know if you'd like this formatted as a completed worksheet!