Which of the following is not true about a wave in a plucked string?

Analysis

The question asks us to identify the property that does not describe a wave produced in a plucked string. To solve this, we must understand the nature of mechanical waves and the specific behavior of waves on a string.

Concept Explanation

1. Mechanical Waves: These are waves that require a material medium (like a string, water, or air) to travel. A plucked string requires the string itself to vibrate, so it is definitely a mechanical wave.
2. Transverse Waves: In a transverse wave, the particles of the medium vibrate perpendicularly (at 90 degrees) to the direction of wave propagation. When you pluck a string, the string moves up and down while the wave travels along the length of the string. This makes it a transverse wave.
3. Crests and Troughs: Because a transverse wave moves in an up-and-down motion, the highest points of the wave are called crests and the lowest points are called troughs. Therefore, a plucked string exhibits crests.
4. Longitudinal Waves: In a longitudinal wave, the particles of the medium vibrate parallel to the direction of the wave (like sound waves in air or a slinky being pushed and pulled). A plucked string does not move in this back-and-forth parallel motion.

Step-by-Step Solution

• Step 1: Evaluate Option A. Since a string is a physical medium, the wave is mechanical. This statement is true.
• Step 2: Evaluate Option B. Transverse waves have crests and troughs. Since the wave is transverse, it has crests. This statement is true.
• Step 3: Evaluate Option C. The vibration of the string is perpendicular to the direction of the wave, which defines a transverse wave. This statement is true.
• Step 4: Evaluate Option D. Longitudinal waves require parallel displacement of particles. Since the string moves perpendicularly, it is not longitudinal. This statement is false.

Conclusion

The question asks for the statement that is not true. Since options A, B, and C are characteristics of a plucked string, option D is the correct choice.

Exam Tip: Remember the mnemonic "T-P" for Transverse = Perpendicular. If the particles move perpendicular to the wave, it is transverse. Longitudinal waves are the opposite—they move parallel to the direction of the wave.