All Exams Test series for 1 year @ ₹349 only
Question

Consider the following statements regarding waves :
1. If the particles of a medium move along the direction of motion of the wave, the wave is called a longitudinal wave.
2. If the particles of a medium move perpendicular to the direction of motion of the wave, the wave is called a transverse wave.
3. Transverse waves may involve change in the shape of the medium, whereas longitudinal waves involve change in the density of the medium.
Which of the statements given above is/are correct ?

This question was previously asked in
CDS 2 2026 Maths Question Paper (13-Sep-2026)
The correct answer is
1, 2 and 3

Wave Statements Analysis

This question asks to identify the correct statements about wave properties, specifically longitudinal and transverse waves.

Statement 1: Longitudinal Wave Definition

  • A longitudinal wave is defined by the motion of the medium's particles.
  • In a longitudinal wave, particles oscillate back and forth parallel to the direction the wave travels.
  • Sound waves are a common example.
  • Therefore, Statement 1 is correct.

Statement 2: Transverse Wave Definition

  • A transverse wave is characterized by particle oscillation relative to wave direction.
  • In a transverse wave, particles move perpendicular to the direction of wave propagation.
  • Examples include light waves and waves on a string.
  • Therefore, Statement 2 is correct.

Statement 3: Wave Characteristics Comparison

  • Transverse waves cause disturbances perpendicular to the wave's path, often leading to changes in the medium's shape (like a ripple on water or a wave on a rope).
  • Longitudinal waves cause compressions and rarefactions parallel to the wave's path, resulting in changes in the medium's density and pressure (like sound).
  • Therefore, Statement 3 is correct.

Conclusion

All three statements accurately describe the properties and definitions of longitudinal and transverse waves.

  • Statement 1: Correct
  • Statement 2: Correct
  • Statement 3: Correct

Thus, all statements (1, 2, and 3) are correct.

Was this answer helpful?

Important Questions from Waves

  1. Which of the following is related to Doppler effect?

  2. The velocity v(x) of a particle moving in one dimension is given by v(x) = v 0 sin \(\rm\left(\frac{\pi x}{x_0}\right) \) , where v 0  and x 0  are positive constants of appropriate dimensions. If the particle is initially at x/x 0  = ϵ, where |ϵ| ≪ 1, then, in the long time, it
  3. The position of a particle in one dimension changes in discrete steps. With each step it moves to the right, however, the length of the step is drawn from a uniform distribution from the interval \(\left[ {{\rm{λ }}\,{\rm{ - }}\,\frac{{\rm{1}}}{{\rm{2}}}{\rm{w,}}\,{\rm{λ }}\,{\rm{ + }}\,\frac{{\rm{1}}}{{\rm{2}}}{\rm{w}}} \right] \) , where λ and w are positive constants. If X denotes the distance from the starting point after N steps, the standard deviation \(\sqrt {\left\langle {{X^2}} \right\rangle \, - {{\left\langle X \right\rangle }^2}} \)  for large values of N is

  4. A particle of mass m in one dimension is in the ground state of a simple harmonic oscillator described by a Hamiltonian \(\frac{{{{\rm{P}}^{\rm{2}}}}}{{{\rm{2m}}}}{\rm{ + }}\frac{{\rm{1}}}{{\rm{2}}}{\rm{m}}{{\rm{\omega }}^{\rm{2}}}{{\rm{x}}^{\rm{2}}} \) in the standard notation. An impulsive force at time t = 0 suddenly imparts a momentum P0 \(\sqrt {{\rm{hm\omega }}} \) to it. The probability that the particle remains in the original ground state is

  5. In an elastic scattering process at an energy E, the phase shifts satisfy δ 0 ≈ 30°, δ 1≈  10°, while the other phase shifts are zero. The polar angle at which the differential cross-section peaks is closest to

Need Expert Advice?
Test Series
CDS img
Defence
UPSC CDS 2026 Mock Test Series
536 Tests 4 Tests Free
1646 Attempts
4.3(174)
English, Hindi
More Questions from CDS

Start Your Preparation with Prepp Mobile App

Download the app from Google Play & App Store
Download the app from Google Play & App Store
Prepp Mobile App