Concepts Of Physics MCQ Edition [Volume 1]PhysicsWave Motion and Waves on a String
When a sine wave travels through a region, two particles A and B exhibit a phase difference of .
Options
- AThe displacements of A and B possess equal magnitudes.
- BParticles A and B move in opposite directions.
- CParticle A oscillates at half the frequency of particle B .
- DThe separation between A and B must be exactly half of the wavelength.
Correct answer
B. Particles A and B move in opposite directions.
Step-by-step solution
Let the equation of the traveling sine wave be y = A ( t - kx) . The phase of a particle at position x is = t - kx . For particles A and B with a phase difference of , we have _A - _B = . The displacements of the particles are: y_A = A ( _A) y_B = A ( _B) = A ( _A - ) = -A ( _A) = -y_A Since y_B = -y_A , the magnitudes of their displacements are always equal ( |y_A| = |y_B| ). The velocities of the particles are: v_A = dy_A dt = A ( _A) v_B = dy_B dt = A ( _A - ) = -A ( _A) = -v_A Since v_B = -v_A , the particles a