Oscillations Waves and Sound 1 An object swings

Oscillations Waves and Sound

1. An object swings on the end of a cord as a simple pendulum with period T. Another object oscillates up and down on the end of a vertical spring also with period T. If the masses of both objects are doubled, what are the new values for the Periods? B

2. An object is attached to a spring and oscillates with amplitude A and period T, as represented on the graph. The nature of the velocity v and acceleration a of the object at time T/4 is best represented by which of the following? (A) v > 0, a > 0 (B) v > 0, a < 0 (C) v > 0, a = 0 (D) v = 0, a < 0 D At T/4 the mass reaches maximum + displacement where the restoring force is at a maximum and pulling in the opposite direction and hence creating a negative acceleration. At maximum displacement the mass stops momentarily and has zero velocity

3. A particle oscillates up and down in simple harmonic motion. Its height y as a function of time t is shown in the diagram. At what time t does the particle achieve its maximum positive acceleration? (A) 1 s (B) 2 s (C) 3 s (D) 4 s A + Acceleration occurs when the mass is at negative displacements since the force will be acting in the opposite direction of the displacement to restore equilibrium. Based on F=k∆x the largest force, and therefore the largest acceleration occurs at the largest displacement

4. Which of the following is true for both spheres? A) The maximum kinetic energy is attained as the sphere passes through its equilibrium position B) The maximum kinetic energy is attained as the sphere reaches its point of release. C) The minimum gravitational potential energy is attained as the sphere passes through its equilibrium position. D) The maximum gravitational potential energy is attained when the sphere reaches its point of release. (E) The maximum total energy is attained only as the sphere passes through its equilibrium position. A For the spring, equilibrium is shown where the maximum transfer of kinetic energy has occurred and likewise for the pendulum the bottom equilibrium position has the maximum transfer of potential energy into spring energy.

5. If both spheres have the same period of oscillation, which of the following is an expression for the spring constant D Set period formulas equal to each other and rearrange for k

6. A simple pendulum and a mass hanging on a spring both have a period of 1 s when set into small oscillatory motion on Earth. They are taken to Planet X, which has the same diameter as Earth but twice the mass. Which of the following statements is true about the periods of the two objects on Planet X compared to their periods on Earth? (A) Both are shorter. (B) Both are the same. (C) The period of the mass on the spring is shorter; that of the pendulum is the same. (D) The period of the pendulum is shorter; that of the mass on the spring is the same D In a mass-spring system, both mass and spring constant (force constant) affect the period.

A 0. l -kilogram block is attached to an initially unstretched spring of force constant k = 40 newtons per meter as shown above. The block is released from rest at time t = 0. 7 A As such the maximum stretch bottom location represents twice the amplitude so simply halving that max ∆x will give the amplitude. Finding the max stretch: The initial height of the box h and the stretch ∆x have the same value (h=∆x)U = Usp mg(∆x 1) = ½ k∆x 12 mg = ½ k ∆x 1 =. 05 m. This is 2 A, so the amplitude is 0. 025 m or 1/40 m.

A 0. l -kilogram block is attached to an initially unstretched spring of force constant k = 40 newtons per meter as shown above. The block is released from rest at time t = 0. 8. What is the resulting period of oscillation? C Plug into period for mass-spring system T = 2π √(m/k)

10. A mass m is attached to a vertical spring stretching it distance d. Then, the mass is set oscillating on a spring with an amplitude of A, the period of oscillation is proportional to D

11. A pendulum with a period of 1 s on Earth, where the acceleration due to gravity is g, is taken to another planet, where its period is 2 s. The acceleration due to gravity on the other planet is most nearly (A) g/4 (B) g/2 (C) 2 g (D) 4 g A Based on T = 2π √(L/g), ¼ g would double the period

12. An ideal massless spring is fixed to the wall at one end, as shown above. A block of mass M attached to the other end of the spring oscillates with amplitude A on a frictionless, horizontal surface. The maximum speed of the block is vm. The force constant of the spring is D

Waves and Sound MC

1. A string is firmly attached at both ends. When a frequency of 60 Hz is applied, the string vibrates in the standing wave pattern shown. Assume the tension in the string and its mass per unit length do not change. Which of the following frequencies could NOT also produce a standing wave pattern in the string? A)30 Hz B) 40 Hz C) 80 Hz D) 180 Hz

2. If the frequency of sound wave is doubled, the wavelength: A. B. C. D. halves and the speed remains unchanged. doubles and the speed remains unchanged. halves and the speed halves. doubles and the speed doubles.

3. The standing wave pattern diagrammed to the right is produced in a string fixed at both ends. The speed of waves in the string is 2 m/s. What is the frequency of the standing wave pattern? A) 0. 25 Hz B) 1 Hz C) 2 Hz D) 4 Hz

4. Two waves pulses approach each other as seen in the figure. The wave pulses overlap at point P. Which diagram best represents the appearance of the wave pulses as they leave point P? A. B. C. D.

5. When the speed of sound in air is 340 m/s, What length of open organ pipe will have a fundamental resonate frequency of 136 Hz ? A) 0. 40 m B) 0. 80 m C) 1. 25 m D) 2. 5 m

6. As sound travels from steel into air, both its speed and its: A) B) C) D) wavelength increase wavelength decrease frequency increase frequency remain unchanged