What is the distance between a compression and its nearest rarefaction in a longitudinal wave?

Options

A. wavelength
B. twice of wavelength
C. half of the wavelength
D. one fourth tof the wavelength

Answer

To find the distance between a compression and its nearest rarefaction in a longitudinal wave, follow these steps:

### Step 1: Understand the Structure of Longitudinal Waves
Longitudinal waves consist of compressions and rarefactions. Compressions are regions where particles are close together, while rarefactions are regions where particles are spread apart.

**Hint:** Recall that longitudinal waves are different from transverse waves, which have crests and troughs.

### Step 2: Define the Wavelength
The wavelength (λ) of a longitudinal wave is defined as the distance over which the wave's shape repeats. In the case of a longitudinal wave, one complete wave consists of one compression followed by one rarefaction.

**Hint:** Think of the wavelength as the distance from one peak of the wave to the next peak.

### Step 3: Relate Compressions and Rarefactions to Wavelength
In a longitudinal wave, the distance from one compression to the next compression is equal to the wavelength (λ). Similarly, the distance from one rarefaction to the next rarefaction is also equal to the wavelength (λ).

**Hint:** Visualize the wave: if you can identify one compression and one rarefaction, you can see how they relate to the wavelength.

### Step 4: Calculate the Distance Between Compression and Rarefaction
Since one complete wave consists of one compression and one rarefaction, the distance between a compression and its nearest rarefaction is half of the wavelength (λ/2).

**Hint:** Remember that you are measuring from the center of one compression to the center of the nearest rarefaction.

### Step 5: Conclusion
Thus, the distance between a compression and its nearest rarefaction in a longitudinal wave is λ/2.

**Final Answer:** The distance between a compression and its nearest rarefaction is half of the wavelength (λ/2).

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