Pick out the correct statement in the following with reference to stationary wave pattern.

Options

A. In a tube open at both end, all the harmonics are present
B. In a tube open at one end, only even harmonics are present
C. The distance between successive nodes is equal to the wavelength
D. In a stretched string, the first overtone is the same as the second harmonic.

Explanation

To solve the question regarding stationary wave patterns, we need to analyze the statements provided and determine which one is correct. Let's break down the concepts step by step:

### Step 1: Understanding Stationary Waves
Stationary waves, also known as standing waves, are formed by the interference of two waves traveling in opposite directions. They are characterized by nodes (points of no displacement) and antinodes (points of maximum displacement).

### Step 2: Analyzing the Open Organ Pipe
1. **Open at Both Ends**: In an open organ pipe, both ends are open, allowing for the formation of antinodes at both ends.
- The fundamental frequency (first harmonic) has a wavelength (λ) equal to twice the length of the pipe (L), i.e., \( λ = 2L \).
- Higher harmonics can also be formed, and both odd and even harmonics are present.

### Step 3: Analyzing the Closed Organ Pipe
2. **Closed at One End**: In a closed organ pipe, one end is closed, which means there is a node at the closed end and an antinode at the open end.
- The fundamental frequency (first harmonic) has a wavelength equal to four times the length of the pipe, i.e., \( λ = 4L \).
- Only odd harmonics are present in this case.

### Step 4: Evaluating the Statements
Now, let's evaluate the statements provided in the question:

1. **"If the tube is open at one end, only even harmonics are present."**
- This statement is **incorrect**. For a tube closed at one end, only odd harmonics are present.

2. **"The distance between successive nodes is equal to the wavelength."**
- This statement is **incorrect**. The distance between successive nodes is equal to half the wavelength, \( \frac{λ}{2} \).

3. **"In a stretched string, the first overtone is the same as the second harmonic."**
- This statement is **correct**. The first overtone corresponds to the second harmonic in a stretched string.

### Conclusion
The correct statement regarding stationary wave patterns is:
- **"In a stretched string, the first overtone is the same as the second harmonic."**