Physics Waves ETEA 2023
PMDC Verified Question 41 of 125
A string clamped at its both ends, vibrates in four segments (loops). The length of string is 150 cm. The wavelength of the wave is:
A
33.3 cm
B
66.7 cm
C
150 cm
D
75 cm
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option D: 75 cm
Concept:

When a string clamped at both ends vibrates, it forms a standing wave composed of discrete segments (loops). Each individual segment corresponds to exactly half a wavelength.

Formula:

$$ L = n \left( \frac{\lambda}{2} \right) $$

Solution:

  • We are given the total length \( L = 150 \text{ cm} \) and the number of loops \( n = 4 \).


  • Set up the equation: \( 150 = 4 \left( \frac{\lambda}{2} \right) \).


  • Simplify the right side: \( 150 = 2\lambda \).


  • Solve for wavelength: \( \lambda = \frac{150}{2} = 75 \text{ cm} \).


Why other options are incorrect:

Option A (33.3 cm) occurs if one divides 150 by 4, incorrectly assuming one loop = one full wavelength. Option C assumes wavelength equals the string length.

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