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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.
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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**.
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**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.**
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Simplify this solution Mind Expander
To determine the frequency of wave a, you can use the formula: Frequency (f) = Speed (v) / Wavelength (λ). If you know the speed of the wave and its wavelength, simply divide the speed by the wavelength to find the frequency. For example, if the wave travels at 300 m/s and has a wavelength of 1.5 m, the frequency would be 200 Hz. In real-world applications, the concept of frequency can be found everywhere! For instance, in music, the frequency of sound waves determines the pitch of the notes we hear. Higher frequencies produce higher pitches, while lower frequencies create lower pitches. So next time you jam to your favorite song, remember there’s a symphony of frequencies at play!
