Concepts Of Physics MCQ Edition [Volume 1]PhysicsWave Motion and Waves on a String
The length of the wire between the pulleys, as shown in the figure, is 1.5 m , and its mass is 12.0 g . Determine the frequency of vibration when the wire vibrates in two loops, leaving the middle point of the wire between the pulleys at rest.
Options
- A35 Hz
- B70 Hz
- C105 Hz
- D140 Hz
Correct answer
B. 70 Hz
Step-by-step solution
Given: Length of the wire, L = 1.5 m Mass of the wire, m = 12.0 g = 12 10⁻³ kg Mass of the hanging blocks, M = 9 kg The linear mass density of the wire is: = m L = 12 10⁻³ 1.5 = 8 10⁻³ kg/m The tension in the wire is provided by the hanging mass (taking g = 9.8 m/s ^2 ): T = Mg = 9 9.8 = 88.2 N The speed of the transverse wave in the wire is: v = T = 88.2 8 10⁻³ = 11025 = 105 m/s Since the wire vibrates in two loops, there is a node at the center. The length of the wire corresponds to two half-wavelengths: L = 2 (