1.5 Determine the frequency of wave a

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It looks like you're referring to a specific problem labeled as **1.5(a)** related to determining the frequency of a wave. To provide a precise answer, I'll need more details about the wave in question. However, I can certainly guide you through the general process of finding a wave's frequency.

### **Understanding Wave Frequency**

**Frequency (f)** is one of the fundamental properties of a wave and is defined as the number of cycles or oscillations that occur in a unit of time. The standard unit of frequency is the **Hertz (Hz)**, where:

$$ 1 \text{ Hz} = 1 \text{ cycle per second} $$

### **Key Relationships Involving Frequency**

1. **Wave Speed, Wavelength, and Frequency:**

The relationship between the wave's speed ($$v$$), wavelength ($$\lambda$$), and frequency ($$f$$) is given by the formula:

$$
   v = f \times \lambda
   $$

- **$$v$$**: Speed of the wave (meters per second, m/s)
   - **$$ \lambda $$**: Wavelength (meters, m)
   - **$$ f $$**: Frequency (Hertz, Hz)

**To find the frequency:**

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

2. **Frequency and Period:**

The **period (T)** is the time it takes for one complete cycle of the wave. The relationship between frequency and period is:

$$
   f = \frac{1}{T}
   $$

- **$$ T $$**: Period (seconds, s)

### **Steps to Determine Frequency**

Depending on the information provided in your problem, you can determine the frequency using one of the following methods:

1. **If You Know Wave Speed and Wavelength:**

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

- **Example:**
     - Wave speed, $$ v = 300 \, \text{m/s} $$
     - Wavelength, $$ \lambda = 0.5 \, \text{m} $$
     - **Frequency, $$ f = \frac{300}{0.5} = 600 \, \text{Hz} $$**

2. **If You Know the Period:**

$$
   f = \frac{1}{T}
   $$

- **Example:**
     - Period, $$ T = 0.02 \, \text{s} $$
     - **Frequency, $$ f = \frac{1}{0.02} = 50 \, \text{Hz} $$**

3. **If You Have Both Speed and Frequency:**

If for some reason you need to find wavelength when given frequency and speed, you can rearrange the first formula:

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

### **Additional Considerations**

- **Types of Waves:** The formulas above apply to all types of waves, including sound waves, light waves, and mechanical waves on a string.
  
- **Medium:** Ensure that the wave speed corresponds to the medium through which the wave is traveling, as wave speed can vary between different media.

### **Example Problem**

**Problem:** A sound wave travels through air at a speed of $$ 343 \, \text{m/s} $$ and has a wavelength of $$ 0.5 \, \text{m} $$. What is its frequency?

**Solution:**

Using the formula $$ f = \frac{v}{\lambda} $$:

$$
f = \frac{343 \, \text{m/s}}{0.5 \, \text{m}} = 686 \, \text{Hz}
$$

**Answer:** The frequency of the wave is **686 Hz**.

---

**If you provide the specific details of Problem 1.5(a), such as the wave's speed, wavelength, or any other given parameters, I can offer a more tailored solution.**
To determine the frequency of wave a, you need to know either the wave's speed and wavelength or the period. Use the formula $$ f = \frac{v}{\lambda} $$ if you have speed and wavelength, or $$ f = \frac{1}{T} $$ if you have the period.

1.5 Determine the frequency of wave a

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