Concepts Of Physics MCQ Edition [Volume 1]PhysicsWave Motion and Waves on a String
A wave travelling on a string has the equation y = (0.10 mm ) [(31.4 m ⁻¹)x + (314 s ⁻¹)t] . What is the maximum displacement and the maximum speed of a portion of the string?
Options
- A0.20 mm and 3.14 cm s ⁻¹
- B0.10 mm and 1.57 cm s ⁻¹
- C0.10 mm and 3.14 cm s ⁻¹
- D0.10 mm and 31.4 cm s ⁻¹
Correct answer
C. 0.10 mm and 3.14 cm s ⁻¹
Step-by-step solution
The standard equation of a travelling wave is given by y = A (kx + t) . Comparing the given equation y = (0.10 mm ) [(31.4 m ⁻¹)x + (314 s ⁻¹)t] with the standard equation, we get: Amplitude A = 0.10 mm Angular frequency = 314 s ⁻¹ The maximum displacement of a portion of the string is its amplitude, which is A = 0.10 mm . The maximum speed of a portion of the string (maximum particle velocity) is given by v_ max = A . Substituting the values: v_ max = (0.10 mm ) (314 s ⁻¹) = 31.4 mm s ⁻¹ Converting to cm s ⁻¹ : v_