Concepts Of Physics MCQ Edition [Volume 1]PhysicsWave Motion and Waves on a String
A wave is described by the equation y = (1.0 mm ) ( x 2.0 cm - t 0.01 s ) . Find the speed of the particle at x = 1.0 cm at time t = 0.01 s .
Options
- A5 cm s ⁻¹
- Bzero
- C10 cm s ⁻¹
- D20 cm s ⁻¹
Correct answer
B. zero
Step-by-step solution
The given wave equation is: y = (1.0 mm ) ( x 2.0 cm - t 0.01 s ) The particle velocity is given by the partial derivative of displacement with respect to time: v_p = y t = (1.0 mm ) ( x 2.0 - t 0.01 ) (- 0.01 ) Substituting x = 1.0 cm and t = 0.01 s : v_p = -100 ( 1.0 2.0 - 0.01 0.01 ) v_p = -100 ( 2 - ) v_p = -100 (- 2 ) Since (- 2 ) = 0 , we get: v_p = 0 Thus, the speed of the particle is zero.