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.

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