1. The overall length of a piccolo is 32.0 cm. The resonating air column vibrates as in a pipe that is open at both ends. Assume the speed of sound is 343 m/s.

a. Find the frequency of the lowest note a piccolo can play (all holes are blocked)

b. Find next three resonant modes of the piccolo when all the holes are blocked

c. Draw diagrams of lowest 4 resonant modes, labeling all nodes and antinodes.

d. Opening holes in the side effectively shortens the length of the resonant column. If the highest note a piccolo can sound is 4 000 Hz, find the distance between adjacent antinodes for this mode of vibration.

Hint: The ends of the piccolo are antinodes in air movement.

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2. and only part d of this question: A 326-g object is attached to a spring and executes simple harmonic motion with a period of T= 0.250 s. If the total energy of the system is 5.83 J, find:

a. The maximum speed of the object.

b. The force constant of the spring

c. The amplitude of the motion

d. the maximum acceleration of the object

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3. Consider the Universe to be spherical, mostly hydrogen gas molecules undergoing adiabatic expansion over its lifetime.

a. Using the ideal gas law and properties of adiabatic processes show T V γ − 1= C where C is a constant.

b. The current Universe extends at least 15 billion light-years in all directions (r = 1.4 x 10²⁶m), and the current temperature of the Universe is 2.7 K. Estimate the temperature of the Universe when it was the size of a nutshell, with a radius of 2 cm.

c. If the density of the gas in the Universe, N/V, is one hydrogen atom per cubic meter, calculate the current pressure of the Universe.

d. Estimate the pressure of the Universe when it was the size of a nutshell. (You may get a calculator overflow error)

Solutions

Expert Solution

genius_generous answered 1 year ago

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