Q: A sound intensity level is measured at $$\beta = 80\ \mathrm{dB}. $$What is the corresponding intensity $$I in$$ $$\mathrm{W/m^2$}$$?

$$I = 1.0 \times 10$$^{-4}$$\ \mathrm{W/m^2$}$$

Q: A 0.25 kg sample of water at $$100^\circ\mathrm{C} is $$converted to steam at $$100^\circ\mathrm{C}. $$How much heat is required? ($$L_v = 2.256 \times 10^6$\ \mathrm{J/kg})$$

$$Q = 5.64 \times 10^5$\ \mathrm{J}$$

Q: A gas is compressed at constant temperature from $$V_1 = 2.0$$\ \mathrm{L}$$ to V_2$ = 1.0\ \mathrm{L}. If $$the initial pressure is $$p_1 = 1.0$$ \times $$10^5$$\ \mathrm{Pa}$$, what is the final pressure?

$$p_2 = 2.0$$ \times $$10^5$$\ \mathrm{Pa}$$

Question 1

A string fixed at both ends has a length $$L = 2.0\ \mathrm{m}$$ and a mass per unit length $$\mu = 0.01\ \mathrm{kg/m}. If $$the tension in the string is $$F_T = 80\ \mathrm{N}$$, what is the frequency of the second harmonic ($$n=2$$)?

Accepted Answer

$$f_2 = 20$$\ \mathrm{Hz}$$

Question 2

A sound source emits a power of $$P = 2.0\ \mathrm{W}. $$What is the intensity $$I at a $$distance $$r = 4.0\ \mathrm{m}$$ from the source?

Accepted Answer

$$I = 0.01\ \mathrm{W/m^2$}$$

Question 3

A 0.5 kg block of ice at $$0^\circ\mathrm{C} is $$placed in contact with $$Q = 2.0 	imes 10^5$\ \mathrm{J} of $$heat. How much ice (in kg) remains after all the heat is absorbed? ($$L_f = 3.34 	imes 10^5$\ \mathrm{J/kg})$$

Accepted Answer

$$0.00\ \mathrm{kg}$$

Question 4

A gas undergoes an isothermal expansion from $$V_1 = 1.0$$\ \mathrm{L}$$ to V_2$ = 3.0\ \mathrm{L} at$$ $$T = 300\ \mathrm{K}. If$$ $$n = 0.5$$ mol, what is the work done by the gas? ($$R = 8.314\ \mathrm{J/(mol\cdot K)})$$

Accepted Answer

$$W = 1379\ \mathrm{J}$$

Question 5

A sound wave travels through air at $$v = 340\ \mathrm{m/s}$$ and has a frequency $$f = 1700\ \mathrm{Hz}. $$What is its wavelength?

Accepted Answer

$$\lambda = 0.2\ \mathrm{m}$$

Question 6

A 2.0 kg block of copper ($$c = 385\ \mathrm{J/(kg\cdot K)}) at$$ $$100^\circ\mathrm{C} is $$placed in $$1.0\ \mathrm{kg} of $$water at $$20^\circ\mathrm{C}$$ ($$c = 4190\ \mathrm{J/(kg\cdot K)}). $$What is the final equilibrium temperature (to the nearest degree Celsius)?

Accepted Answer

$$T_f = 32^\circ\mathrm{C}$$

Question 7

A closed container holds $$0.1$$ mol of an ideal monatomic gas at $$T = 300\ \mathrm{K}. $$What is the average translational kinetic energy of the gas?

Accepted Answer

$$K_{tr} = 374\ \mathrm{J}$$

Question 8

A sound source moves toward a stationary observer at $$v_S = 20\ \mathrm{m/s}$$ ($$v = 340\ \mathrm{m/s}). If $$the source emits $$f_S = 500\ \mathrm{Hz}$$, what frequency does the observer hear?

Accepted Answer

$$f_L = 531\ \mathrm{Hz}$$

Question 9

A 0.2 kg aluminum rod ($$c = 900\ \mathrm{J/(kg\cdot K)}) at$$ $$150^\circ\mathrm{C} is $$dropped into $$0.5\ \mathrm{kg} of $$water at $$20^\circ\mathrm{C}. $$What is the final temperature, assuming no heat loss?

Accepted Answer

$$T_f = 32^\circ\mathrm{C}$$

Question 10

A standing wave on a string fixed at both ends has a frequency of $$120\ \mathrm{Hz}$$ and a length $$L = 0.75\ \mathrm{m}. If $$the wave speed is $$v = 180\ \mathrm{m/s}$$, what harmonic is being produced?

Accepted Answer

$$n = 3$$

Question 11

A gas is compressed adiabatically so that its volume decreases to half its original value. If $$\gamma = 1.4$$, by what factor does the pressure increase?

Accepted Answer

$$2.64$$

Question 12

A 0.1 mol sample of an ideal gas is heated at constant pressure from $$T_1 = 300$$\ \mathrm{K}$$ to T_2$ = 600\ \mathrm{K}. $$What is the change in internal energy $$\Delta U$$?

Accepted Answer

$$\Delta U = 1247\ \mathrm{J}$$

Question 13

A 0.5 kg block of ice at $$-10^\circ\mathrm{C} is $$heated until it becomes water at $$0^\circ\mathrm{C}. $$How much heat is required? ($$c_{ice} = 2010\ \mathrm{J/(kg\cdot K)})$$

Accepted Answer

$$Q = 10,050\ \mathrm{J}$$

Question 14

A 1.0 L container holds oxygen gas ($$M = 0.032\ \mathrm{kg/mol}) at$$ $$p = 2.0 	imes 10^5$\ \mathrm{Pa}$$ and $$T = 300\ \mathrm{K}. $$What is the mass of oxygen in the container?

Accepted Answer

$$m = 2.56\ \mathrm{g}$$

Question 15

A pipe open at both ends has a length $$L = 0.85\ \mathrm{m}. $$What is the fundamental frequency if the speed of sound is $$v = 340\ \mathrm{m/s}$$?

Accepted Answer

$$f_1 = 200$$\ \mathrm{Hz}$$

Question 16

A sound intensity level is measured at $$\beta = 80\ \mathrm{dB}. $$What is the corresponding intensity $$I in$$ $$\mathrm{W/m^2$}$$?

Accepted Answer

$$I = 1.0 	imes 10$$^{-4}$$\ \mathrm{W/m^2$}$$

Question 17

A 0.25 kg sample of water at $$100^\circ\mathrm{C} is $$converted to steam at $$100^\circ\mathrm{C}. $$How much heat is required? ($$L_v = 2.256 	imes 10^6$\ \mathrm{J/kg})$$

Accepted Answer

$$Q = 5.64 	imes 10^5$\ \mathrm{J}$$

Question 18

A gas is compressed at constant temperature from $$V_1 = 2.0$$\ \mathrm{L}$$ to V_2$ = 1.0\ \mathrm{L}. If $$the initial pressure is $$p_1 = 1.0$$ 	imes $$10^5$$\ \mathrm{Pa}$$, what is the final pressure?

Accepted Answer

$$p_2 = 2.0$$ 	imes $$10^5$$\ \mathrm{Pa}$$

Question 19

A 0.3 kg block of ice at $$0^\circ\mathrm{C} is $$placed in $$0.5\ \mathrm{kg} of $$water at $$20^\circ\mathrm{C}. $$What is the final temperature after thermal equilibrium is reached? ($$c_{water} = 4190\ \mathrm{J/(kg\cdot K)}$$, $$L_f = 3.34 	imes 10^5$\ \mathrm{J/kg})$$

Accepted Answer

$$T_f = 0^\circ\mathrm{C}$$

Question 20

A 1.0 kg block of ice at $$-20^\circ\mathrm{C} is $$heated until it becomes water at $$0^\circ\mathrm{C}. $$How much heat is required? ($$c_{ice} = 2010\ \mathrm{J/(kg\cdot K)})$$

Accepted Answer

$$Q = 40,200\ \mathrm{J}$$

Equations and Concepts for Mechanical Waves, Sound, Fluid Mechanics, and Thermodynamics (Chapters 12-15)

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