The distance between 5 crests is 40 m . a) What is the frequency of the waves? b) What is the wavelength of the waves? c) Calculate the wave speed.

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To solve the given wave-related problems, we'll analyze each part step-by-step.

### Given:
- **Distance between 5 crests:** 40 meters

### Understanding the Basics:
1. **Crests and Wavelength:**
   - In a wave, **wavelength (λ)** is the distance between two consecutive crests (or troughs).
   - If you have multiple crests, the total distance between them can help determine the wavelength.

2. **Wave Speed and Frequency:**
   - **Wave speed (v):** How fast the wave propagates through a medium.
   - **Frequency (f):** The number of crests passing a point per second.
   - **Relationship:** $$ v = f \times \lambda $$

### Part (b): Wavelength of the Waves

**Step-by-Step Solution:**
1. **Determine the Number of Wavelengths:**
   - **5 crests** mean there are **4 wavelengths** between them. (Between crest 1 to crest 2 is one wavelength, crest 2 to crest 3 is another, and so on.)

2. **Calculate Wavelength (λ):**
   $$
   \lambda = \frac{\text{Total Distance}}{\text{Number of Wavelengths}} = \frac{40 \, \text{m}}{4} = 10 \, \text{meters}
   $$

**Answer:**
- **Wavelength (λ) = 10 meters**

---

### Part (a) and (c): Frequency and Wave Speed

**Issue:**
- To determine **frequency (f)** and **wave speed (v)**, we need more information, specifically the **time** it takes for the waves to pass a certain point or the **wave speed** itself.

**Why We Can't Proceed:**
- **Frequency (f):** Relates to how many crests pass a point per unit time. Without knowing the time interval, it's impossible to calculate.
- **Wave Speed (v):** Relates to both frequency and wavelength. Without either frequency or wave speed, we can't determine the other.

**What’s Needed:**
- **Additional Information:** Such as the time it takes for a certain number of crests to pass a fixed point or the speed at which the wave is traveling.

**Answer:**
- **Frequency (f):** Cannot be determined with the given information.
- **Wave Speed (v):** Cannot be determined with the given information.

---

### Summary of Answers:

**a) Frequency of the waves:**
- Cannot be determined with the given information.

**b) Wavelength of the waves:**
- **10 meters**

**c) Wave speed:**
- Cannot be determined with the given information.
- **Wavelength:** 10 meters - **Frequency and Wave Speed:** Cannot be determined with the given information.

The distance between 5 crests is 40 m . a) What is the frequency of the waves? b) What is the wavelength of the waves? c) Calculate the wave speed.

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