Question

In a longitudinal wave, the distance between a compression and its adjacent rarefaction is

• A. $\lambda$
• B. $\lambda/2$
• C. $\lambda/4$
• D. $2\lambda$
• E. $3\lambda/4$

Hint:

This is exactly analogous to transverse waves, where the distance from a crest to the very next trough is $\lambda/2$. Always remember that the full "pattern" requires one of each high and low point.

Answer 1

The Correct Option is B

Concept:
Physics - Wave Motion and Wavelength.
Step 1: Define Wavelength ($\lambda$) for longitudinal waves.
For a longitudinal wave, the wavelength is the distance between two consecutive points in the same phase. This is typically measured as the distance between two consecutive compressions or two consecutive rarefactions.
Step 2: Analyze the wave structure.
One complete cycle of a longitudinal wave consists of one compression followed by one rarefaction. [Image of a longitudinal wave showing compression and rarefaction]
Step 3: Calculate the distance between adjacent opposite phases.
Since a full cycle (compression to next compression) is $\lambda$, the distance from a compression to the midpoint of the next rarefaction is exactly half of that cycle. $$ \text{Distance} = \frac{\lambda}{2} $$