A standing wave in a string 35 cm long has a total of six nodes including those at the ends. Hence, wavelength of the standing wave is

Options

A. 5.8 cm
B. 4.6 cm
C. 10.4 cm
D. 14 cm

Explanation

To find the wavelength of the standing wave in a string that is 35 cm long and has a total of 6 nodes (including those at the ends), we can follow these steps:

### Step 1: Understand the relationship between nodes and wavelength
In a standing wave, the number of nodes (N) is related to the wavelength (λ) and the length of the string (L) by the formula:
\[ L = \frac{(N - 1) \cdot \lambda}{2} \]
where \(N\) is the total number of nodes.

### Step 2: Identify the values from the problem
From the problem, we have:
- Length of the string, \(L = 35 \, \text{cm}\)
- Total number of nodes, \(N = 6\)

### Step 3: Substitute the values into the formula
Now, we can substitute the known values into the formula:
\[ 35 = \frac{(6 - 1) \cdot \lambda}{2} \]

### Step 4: Simplify the equation
Calculating \(6 - 1\):
\[ 35 = \frac{5 \cdot \lambda}{2} \]

### Step 5: Multiply both sides by 2 to eliminate the fraction
\[ 70 = 5 \cdot \lambda \]

### Step 6: Solve for λ
Now, divide both sides by 5:
\[ \lambda = \frac{70}{5} \]
\[ \lambda = 14 \, \text{cm} \]

### Conclusion
The wavelength of the standing wave is \(14 \, \text{cm}\).

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