Standing waves are produced by the interference of two traveling sinusoidal waves, each of frequency 100 Hz. The distance from the 2nd node to the 5th node is 60 cm. The wavelength of each of the two original waves is

Options

A. 50cm
B. 40cm
C. 30cm
D. 20cm

Answer

To find the wavelength of each of the two original waves that produce standing waves, we can follow these steps:

### Step 1: Understand the Node Concept
In a standing wave pattern, nodes are points where there is no displacement. The distance between two consecutive nodes is equal to half the wavelength (λ/2).

### Step 2: Identify the Nodes
Given that the distance from the 2nd node to the 5th node is 60 cm, we can identify how many nodes are involved:
- From the 2nd node to the 5th node, there are 3 nodes: 2nd, 3rd, 4th, and 5th.

### Step 3: Count the Half Wavelengths
The distance between the 2nd and 5th nodes includes 3 segments of λ/2:
- The distance between the 2nd and 3rd nodes is λ/2,
- The distance between the 3rd and 4th nodes is λ/2,
- The distance between the 4th and 5th nodes is λ/2.

Thus, the total distance from the 2nd to the 5th node can be expressed as:
\[ \text{Distance} = 3 \times \frac{\lambda}{2} \]

### Step 4: Set Up the Equation
We know from the problem that this distance is 60 cm:
\[ 3 \times \frac{\lambda}{2} = 60 \text{ cm} \]

### Step 5: Solve for Wavelength (λ)
To find λ, we can rearrange the equation:
\[ \frac{3\lambda}{2} = 60 \]
Multiplying both sides by 2:
\[ 3\lambda = 120 \]
Now, divide both sides by 3:
\[ \lambda = \frac{120}{3} = 40 \text{ cm} \]

### Conclusion
The wavelength of each of the two original waves is **40 cm**.

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