b) What is the period of the waves?
A boy on a harbour wall watches the sea waves that move past hi
times the waves and finds that a crest moves past him every 5 sec
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.

Question

UpStudy AI · Accepted Answer

Certainly! Let's analyze the given problem step by step to find the frequency, wavelength, and wave speed of the sea waves observed by the boy.

### **Given:**
1. **Time between successive crests (Period, $$ T $$)**: 5 seconds
2. **Distance between 5 crests**: 40 meters

### **Understanding the Problem:**

- **Period ($$ T $$)**: The time it takes for one complete wave cycle (from one crest to the next).
- **Frequency ($$ f $$)**: The number of wave cycles passing a point per unit time.
- **Wavelength ($$ \lambda $$)**: The distance between consecutive crests (or any two identical points) of the wave.
- **Wave Speed ($$ v $$)**: The speed at which the wave propagates through the medium.

### **Calculations:**

---

#### **a) What is the frequency of the waves?**

**Formula:**
$$ f = \frac{1}{T} $$

**Calculation:**
$$
f = \frac{1}{5 \, \text{seconds}} = 0.2 \, \text{Hz}
$$

**Answer:**
The frequency of the waves is **0.2 Hz**.

---

#### **b) What is the wavelength of the waves?**

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

**Understanding:**
- The distance between 5 crests encompasses **4 wavelengths** (since wavelength is the distance between two consecutive crests).

**Formula:**
$$
\lambda = \frac{\text{Total distance between crests}}{\text{Number of wavelengths}}
$$

**Calculation:**
$$
\lambda = \frac{40 \, \text{meters}}{4} = 10 \, \text{meters}
$$

**Answer:**
The wavelength of the waves is **10 meters**.

---

#### **c) Calculate the wave speed.**

**Formula:**
$$
v = \lambda \times f
$$

**Calculation:**
$$
v = 10 \, \text{meters} \times 0.2 \, \text{Hz} = 2 \, \text{meters/second}
$$

**Alternative Method:**
Wave speed can also be calculated using the distance between crests and the time taken for that distance.

$$
v = \frac{\text{Distance between crests}}{\text{Time taken}}
$$

Here, distance between 5 crests is 40 meters, which corresponds to 4 wavelengths. The time taken for 5 crests is $$ 4 \times 5 \, \text{seconds} = 20 \, \text{seconds} $$.

$$
v = \frac{40 \, \text{meters}}{20 \, \text{seconds}} = 2 \, \text{meters/second}
$$

**Answer:**
The wave speed is **2 meters per second**.

---

### **Summary:**
- **Frequency ($$ f $$)**: 0.2 Hz
- **Wavelength ($$ \lambda $$)**: 10 meters
- **Wave Speed ($$ v $$)**: 2 meters/second
- **Frequency**: 0.2 Hz - **Wavelength**: 10 meters - **Wave Speed**: 2 meters/second

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