Question

Assertion (A): A standing wave is produced in a string clamped at one end and free at the other end. The length of string is odd multiples of $\frac{\lambda}{4}$ Reason (R): Distance between successive node and antinode is $\frac{\lambda}{4}$.

• A. Both assertion and reason are true and reason is the correct explanation of assertion
• B. Both assertion and reason are true but reason is not the correct explanation of assertion
• C. A ssertion is true but reason is false
• D. Both assertion and reason are false

Answer 1

Answer: (B)

At the clamped end always a node is formed and at the tree end, an antinode is formed.
distance between a node and antinode is $\frac{\lambda}{4}$
$\therefore $ so total length is $n \left(\frac{\lambda}{2}\right)+\frac{\lambda}{4}=(2 n +1) \frac{\lambda}{4}$