Physics of Oscillations and Waves Study Questions

Principles of Oscillations and Wave Mechanics

1. A stretched or compressed spring stores elastic potential energy.
2. In the equation for Hooke’s Law, F_elastic = –kx, the term k represents the spring constant of a spring.

3. Kinetic Energy in Oscillating Systems

   At what position of an oscillating mass-spring system does the kinetic energy of the mass reach a maximum?

   The kinetic energy of the mass in an oscillating mass-spring system reaches a maximum at the equilibrium position (center) of the cycle, where the mass is moving at maximum velocity.

4. If a spring is stretched from a displacement of 10 cm to a displacement of 30 cm, the force exerted by the spring increases by a factor of three.

5. Relationship Between Period and Frequency

   How is the relationship between period and frequency represented as an equation?

   f = 1/T

6. Pendulum Period and Gravitational Effects

   Suppose that a pendulum has a period of 4.0 s at Earth’s surface. If the pendulum is taken to the Moon, where the acceleration due to gravity is much less than on Earth, will the pendulum’s period increase, decrease, or stay the same? Explain your answer.

   The period will increase because the restoring force is a component of the gravitational force acting on the pendulum bob (the bob’s weight). Because the restoring force is less, but the mass remains the same, the acceleration of the pendulum bob is less.

7. Mass and Pendulum Period

   A certain pendulum with a 1.00 kg bob has a period of 3.50 s. What will happen to the period of the pendulum if the 1.00 kg bob is replaced by a bob with a mass of 2.00 kg? Explain your answer.

   The period of the pendulum will remain the same. The period of a pendulum depends only on the pendulum’s length, not on its mass.

8. A student observes two pulses on a rope wave meet and temporarily form a wave with a greater amplitude than either of the two waves alone. The student has observed an example of constructive interference.

9. Wave Interference and Fixed Boundaries

   Two pulses of equal positive amplitude travel along a rope toward a fixed boundary. The first pulse is reflected and returns along the rope. When the two pulses meet and coincide, what kind of interference will occur? Explain.

   Complete destructive interference should occur because the first pulse is inverted when it reflects from the fixed boundary. The pulses then meet with equal but opposite amplitudes.