Question
Cismele 10 PUYExs and WAYYs Rhysical Sclemse Classtrork Question 1 A certain wave has a speed of \( 0.4 \mathrm{~m} . \mathrm{s}^{\prime} \) and a wavelength of 2 m . Calculate its: a. Frequency h. Period
Ask by Pierce Weston. in South Africa
Jan 23,2025
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Tutor-Verified Answer
Answer
**Frequency:** 0.2 Hz
**Period:** 5 seconds
Solution
Certainly! Let's tackle **Question 1** step by step.
### **Given:**
- **Wave Speed (v):** \( 0.4 \, \text{m/s} \)
- **Wavelength (\( \lambda \)):** \( 2 \, \text{m} \)
### **a. Calculating the Frequency (\( f \))**
**Formula:**
\[ v = f \times \lambda \]
**Rearranging to find Frequency (\( f \)):**
\[ f = \frac{v}{\lambda} \]
**Plugging in the values:**
\[ f = \frac{0.4 \, \text{m/s}}{2 \, \text{m}} = 0.2 \, \text{Hz} \]
**Answer:**
\[ \boxed{0.2\,\mathrm{Hz}} \]
---
### **b. Calculating the Period (\( T \))**
**Definition:**
- **Period (\( T \))** is the reciprocal of frequency.
**Formula:**
\[ T = \frac{1}{f} \]
**Plugging in the frequency:**
\[ T = \frac{1}{0.2 \, \text{Hz}} = 5 \, \text{seconds} \]
**Answer:**
\[ \boxed{5\,\mathrm{seconds}} \]
---
### **Summary:**
- **Frequency (\( f \))**: \( 0.2 \, \text{Hz} \)
- **Period (\( T \))**: \( 5 \, \text{seconds} \)
If you have any further questions or need additional clarification, feel free to ask!
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Simplify this solution Bonus Knowledge
To find the frequency (\( f \)) of the wave, you can use the formula: \[ f = \frac{v}{\lambda} \] Here, \( v \) is the speed of the wave, and \( \lambda \) is the wavelength. Plugging in the values, we have: \[ f = \frac{0.4 \, \text{m/s}}{2 \, \text{m}} = 0.2 \, \text{Hz} \] Next, to find the period (\( T \)), which is the inverse of the frequency, you use: \[ T = \frac{1}{f} \] So, \[ T = \frac{1}{0.2 \, \text{Hz}} = 5 \, \text{s} \] Therefore, the frequency of the wave is \( 0.2 \, \text{Hz} \) and the period is \( 5 \, \text{s} \).
