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Oscillations, Frequency, Waves, Doppler Effect, etc

1. A 2kg block is attached to a spring and placed on a horizontal smooth surface. A horizontal force of 20N is required to hold the block at rest when it is pulled .2m from its equilibrium position. The block is released from its rest from this point, and is subsequently undergoes simple harmonic motion. Find a) the spring stiffness; b) the frequency of oscillations; c) the maximum speed of the block. Where does this maximum speed occur? Find the total energy of the oscillating system. Find the speed when the position equals one third of the maximum value.

2. A string fixed at both ends and having a mass of 4.8g, a length of 2 m, and a tension of 48N vibrates in its second normal mode. What is the wavelength in the air of the sound emitted by this vibrating string?

3. You stand just to the side of the low point of a childs swing and always push the child in the same direction. Which of the following multiples of the fundamental frequency will produce resonance: 1/3, ½, 1, 2?

4. A longitudinal standing wave can be established in a long aluminum rod by stroking it with rosin on your fingers. If the rod is held tightly at its midpoint, what is the wavelength of the fundamental standing wave? Assume that there are antinodes at each end of the rod and node where the rod is held.

5. An astronaut measures his weight in orbit by sitting on a seat of known mass that oscillates due to springs of known stiffness. The measured period of oscillation determines the total oscillating a) mass, b) weight.

6. Does a car bounce on its springs faster when it is empty or when it is fully loaded?

7. How does the natural frequency of a swing change when you move from sitting down to standing up?

8. Suppose a source of sound moves at right angles to the line of sight of a listener at rest in still air. Will there be a Doppler effect?

9. In the following list of properties of periodic waves, which one is independent of the others: frequency, wavelength, speed, amplitude? What happens to the wavelength if both the speed of the wave and the frequency are cut in half?

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Solution answers 9 mixed sound physics questions showing the necessary steps. Attached as PDF.

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