1. A violin string of length 40 cm and mass 1.2 g has a frequency of 500 Hz when it is vibrating in its fundamental mode. What is the wavelength of the standing wave on the string? What is the tension in the string? Where should you place your finger to increase the frequency to 650 Hz?

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Chapter1: Units, Trigonometry. And Vectors
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1. A violin string of length 40 cm and mass 1.2 g has a frequency of 500 Hz when it is vibrating in its fundamental mode.

  • What is the wavelength of the standing wave on the string?
  • What is the tension in the string?
  • Where should you place your finger to increase the frequency to 650 Hz?

2.An object of mass 2 kg resting on a frictionless horizontal surface is attached to a spring of force constant 600 N/m. A second object of mass 1 kg slides along the surface toward the first object at 6 m/s.

  • Find the amplitude of oscillation if the objects make a perfectly inelastic collision and remain together on the spring. What is the period of oscillation?
  • Find the amplitude and period of oscillation if the collision is elastic?
  • For each type of collision, write an expression for the position x as a function of time t for the object attached to the spring, assuming that the collision occurs at time t = 0. What is the impulse delivered to the 2 kg object in each case?

(The initial conditions are x(0) = 0 and v(0) > 0 )

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