A specific note on a musical instrument hos a frequericy of 359 Hz . Calculate the wavelength of the sound procluced it the speerd of sound in? air is $$ 343 \mathrm{~m}-\mathrm{s}^{1} $$. The wavelength of a longitudinal wave is 0.20 m , and the flime token to complete one wave is 30 seconcls. Calculate the speed at which tree we is travelling.

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Sure, let's tackle both parts of your question step by step.

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### **1. Calculating the Wavelength of the Sound**

**Given:**
- **Frequency (f)** = 359 Hz
- **Speed of Sound in Air (v)** = 343 m/s

**Formula:**
The relationship between speed ($$ v $$), frequency ($$ f $$), and wavelength ($$ \lambda $$) is given by:

$$
v = f \times \lambda
$$

To find the **wavelength ($$ \lambda $$)**, rearrange the formula:

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

**Calculation:**

$$
\lambda = \frac{343 \, \text{m/s}}{359 \, \text{Hz}} \approx 0.956 \, \text{meters}
$$

**Answer:**
The wavelength of the sound produced is approximately **0.956 meters**.

---

### **2. Calculating the Speed of a Longitudinal Wave**

**Given:**
- **Wavelength ($$ \lambda $$)** = 0.20 meters
- **Time to Complete One Wave ($$ T $$)** = 30 seconds

**Understanding the Parameters:**
- The **time to complete one wave ($$ T $$)** is also known as the **period**.
- **Frequency ($$ f $$)** can be calculated as the reciprocal of the period:

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

**Formula:**
The speed ($$ v $$) of a wave is calculated using:

$$
v = \lambda \times f
$$

**Calculations:**

1. **Calculate Frequency ($$ f $$):**

$$
f = \frac{1}{T} = \frac{1}{30 \, \text{seconds}} \approx 0.0333 \, \text{Hz}
$$

2. **Calculate Speed ($$ v $$):**

$$
v = \lambda \times f = 0.20 \, \text{m} \times 0.0333 \, \text{Hz} \approx 0.00667 \, \text{m/s}
$$

**Answer:**
The speed at which the longitudinal wave is traveling is approximately **0.00667 meters per second**.

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### **Summary**

1. **Wavelength of the sound produced by the musical instrument:** ≈ **0.956 meters**
2. **Speed of the longitudinal wave:** ≈ **0.00667 meters per second**

If you have any more questions or need further clarification, feel free to ask!
The wavelength of the sound is approximately 0.956 meters. The speed of the longitudinal wave is about 0.00667 meters per second.

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