Concepts Of Physics MCQ Edition [Volume 1]PhysicsWave Motion and Waves on a String
By sinusoidally vibrating one end of a long horizontal string up and down, a travelling wave is generated. The vibration amplitude is 1.0 cm , and the displacement reaches zero 200 times per second. The string has a linear mass density of 0.10 kg m ⁻¹ and is maintained under a tension of 90 N . The wave propagates in the positive x -direction, and at t = 0 , the end at x = 0 is at its positive extreme position. Deter
Options
- Am s ⁻¹ , -100 ^2 m s ⁻²
- B- m s ⁻¹ , 100 ^2 m s ⁻²
- C3 m s ⁻¹ , -200 ^2 m s ⁻²
- D- 3 m s ⁻¹ , 200 ^2 m s ⁻²
Correct answer
D. - 3 m s ⁻¹ , 200 ^2 m s ⁻²
Step-by-step solution
Given the amplitude A = 1.0 cm = 0.01 m . Since the displacement reaches zero 200 times per second and a sinusoidal wave crosses zero twice per cycle, the frequency is f = 200 2 = 100 Hz . The angular frequency is = 2 f = 200 rad s ⁻¹ . The wave speed is given by v = T = 90 0.10 = 30 m s ⁻¹ . The wave number is k = v = 200 30 = 20 3 m ⁻¹ . The wave propagates in the positive x -direction. At t = 0 and x = 0 , the particle is at its positive extreme, so the wave equation is y(x,t) = A ( t - kx) . We need to find the