In a standing wave, not necessarily at the fundamental frequency, on a string of length L, the distance between nodes is
A) λ/4.
B) λ/2.
C) λ.
D) L/4.
E) L/2.

Question

Quizplus · Accepted Answer

In a standing wave on a string, nodes are points where the amplitude of vibration is zero. In a standing wave with an arbitrary frequency, the wavelength λ will not necessarily be equal to the length L of the string. However, regardless of the frequency, there will always be a node at each end of the string (since the string is fixed at those points), so the distance between these two nodes is equal to the length of the string, or L. Additionally, there will be a node at the midpoint of the string, where the amplitude of vibration is also zero. Therefore, the distance between the two adjacent nodes (one at each end of the string and one at the midpoint) is equal to half the wavelength, or λ/2. Thus, the best answer is B.

In a Standing Wave, Not Necessarily at the Fundamental Frequency