0. Calculate the frequency of a wave with a: 10.1 speed of $$ 200 \mathrm{~m} \cdot \mathrm{~s}^{-1} $$ and a wavelength of 1200 m . 10.2 wavelength of 50 m and a speed of $$ 250 \mathrm{~m} \cdot \mathrm{~s}^{-1} $$. Calculate the wavelength of a wave with $$ \mathrm{a}: $$ 11.1 frequency of 20 Hz and a speed of $$ 120 \mathrm{~m} \cdot \mathrm{~s}^{-1} $$. 11.2 speed of $$ 150 \mathrm{~m} \cdot \mathrm{~s}^{-1} $$ and a frequency of 30 Hz .

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UpStudy AI · Accepted Answer

Sure, let's solve each part step by step using the fundamental wave equation:

$$
v = f \lambda
$$

Where:
- $$ v $$ = wave speed (meters per second, m/s)
- $$ f $$ = frequency (Hertz, Hz)
- $$ \lambda $$ = wavelength (meters, m)

We can rearrange this equation to solve for frequency ($$ f $$) or wavelength ($$ \lambda $$) as needed:
- To find frequency: $$ f = \frac{v}{\lambda} $$
- To find wavelength: $$ \lambda = \frac{v}{f} $$

---

### **10. Calculate the Frequency of a Wave**

#### **10.1** Given:
- **Speed ($$ v $$)** = $$ 200 \, \mathrm{m/s} $$
- **Wavelength ($$ \lambda $$)** = $$ 1200 \, \mathrm{m} $$

**Solution:**
$$
f = \frac{v}{\lambda} = \frac{200 \, \mathrm{m/s}}{1200 \, \mathrm{m}} = \frac{1}{6} \, \mathrm{Hz} \approx 0.167 \, \mathrm{Hz}
$$

**Answer:** The frequency is approximately **0.167 Hz**.

---

#### **10.2** Given:
- **Wavelength ($$ \lambda $$)** = $$ 50 \, \mathrm{m} $$
- **Speed ($$ v $$)** = $$ 250 \, \mathrm{m/s} $$

**Solution:**
$$
f = \frac{v}{\lambda} = \frac{250 \, \mathrm{m/s}}{50 \, \mathrm{m}} = 5 \, \mathrm{Hz}
$$

**Answer:** The frequency is **5 Hz**.

---

### **11. Calculate the Wavelength of a Wave**

#### **11.1** Given:
- **Frequency ($$ f $$)** = $$ 20 \, \mathrm{Hz} $$
- **Speed ($$ v $$)** = $$ 120 \, \mathrm{m/s} $$

**Solution:**
$$
\lambda = \frac{v}{f} = \frac{120 \, \mathrm{m/s}}{20 \, \mathrm{Hz}} = 6 \, \mathrm{m}
$$

**Answer:** The wavelength is **6 meters**.

---

#### **11.2** Given:
- **Speed ($$ v $$)** = $$ 150 \, \mathrm{m/s} $$
- **Frequency ($$ f $$)** = $$ 30 \, \mathrm{Hz} $$

**Solution:**
$$
\lambda = \frac{v}{f} = \frac{150 \, \mathrm{m/s}}{30 \, \mathrm{Hz}} = 5 \, \mathrm{m}
$$

**Answer:** The wavelength is **5 meters**.

---

### **Summary of Results**

| Problem | Given                     | Calculated Value |
|---------|---------------------------|-------------------|
| 10.1    | $$ v = 200 \, \mathrm{m/s} $$, $$ \lambda = 1200 \, \mathrm{m} $$ | $$ f \approx 0.167 \, \mathrm{Hz} $$ |
| 10.2    | $$ v = 250 \, \mathrm{m/s} $$, $$ \lambda = 50 \, \mathrm{m} $$   | $$ f = 5 \, \mathrm{Hz} $$         |
| 11.1    | $$ f = 20 \, \mathrm{Hz} $$, $$ v = 120 \, \mathrm{m/s} $$      | $$ \lambda = 6 \, \mathrm{m} $$    |
| 11.2    | $$ v = 150 \, \mathrm{m/s} $$, $$ f = 30 \, \mathrm{Hz} $$      | $$ \lambda = 5 \, \mathrm{m} $$    |

Feel free to ask if you have any further questions!
**Calculations:** 1. **Frequency Calculations:** - **10.1:** Speed = 200 m/s, Wavelength = 1200 m → Frequency ≈ 0.167 Hz - **10.2:** Wavelength = 50 m, Speed = 250 m/s → Frequency = 5 Hz 2. **Wavelength Calculations:** - **11.1:** Frequency = 20 Hz, Speed = 120 m/s → Wavelength = 6 m - **11.2:** Speed = 150 m/s, Frequency = 30 Hz → Wavelength = 5 m **Summary:** - 10.1: Frequency ≈ 0.167 Hz - 10.2: Frequency = 5 Hz - 11.1: Wavelength = 6 m - 11.2: Wavelength = 5 m

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