Question

A stationary wave is formed having 4 nodes along the $120\,\text{cm$ length of the string. The wavelength of the wave is}

• A. $20\,\text{cm}$
• B. $40\,\text{cm}$
• C. $80\,\text{cm}$
• D. $60\,\text{cm}$

Hint:

Always count the number of intervals between nodes, not the nodes themselves.

Answer 1

The Correct Option is C

Step 1: Relation between nodes and wavelength.
Distance between two consecutive nodes is $\dfrac{\lambda}{2}$.

Step 2: Total number of segments.
If there are 4 nodes, then number of segments between nodes is 3.

Step 3: Writing length of string.
\[ L = 3 \times \frac{\lambda}{2} \]
Step 4: Substituting given length.
\[ 120 = \frac{3\lambda}{2} \] \[ \lambda = 80\,\text{cm} \]
Step 5: Conclusion.
The wavelength of the stationary wave is $80\,\text{cm}$.