Global warming will produce rising sea levels partly due to melting ice caps and partly due to the expansion of water as average ocean temperatures rise. To get some idea of the size of this effect, calculate the change in length of a column of water $1.00 \mathrm{~km}$ high for a temperature increase of $1.00^{\circ} \mathrm{C}$. Assume the column is not free to expand sideways. As a model of the ocean, that is a reasonable approximation, as only parts of the ocean very close to the surface can expand sideways onto land, and only to a limited degree. As another approximation, neglect the fact that ocean warming is not uniform with depth.

Twin jet engines on an airplane are producing an average sound frequency of 4100 Hz with a beat frequency of 0.500 Hz. What are their individual frequencies?

A 2.40-m wire has a mass of 7.50 g and is under a tension of 160 N. The wire is held rigidly at both ends and set into oscillation. (a) What is the speed of waves on the wire? The string is driven into resonance by a frequency that produces a standing wave with a wavelength equal to 1.20 m. (b) What is the frequency used to drive the string into resonance?

A string is 3.00 m long with a mass of 5.00 g. The string is held taut with a tension of 500.00 N applied to the string. A pulse is sent down the string. How long does it take the pulse to travel the 3.00 m of the string?

Consider the wave function

$$y(x, t) = (3.00 cm)sin(0.4 m^{-1}x + 2.00 s^{-1}t + π/10).$$

What are the period, wavelength, speed, and initial phase shift of the wave modeled by the wave function?

A 250-g mass is mounted on a spring of constant k=3.3 N/m. The damping constant for this system is $b=8.4 \times 10^{-3} \mathrm{~kg} / \mathrm{s}$. How many oscillations will the system undergo before the amplitude decays to $1 / e$ of its original value?

Suppose you have a 0.750-kg object on a horizontal surface connected to a spring that has a force constant of 150 N/m. There is simple friction between the object and surface with a static coefficient of friction

$$μ_s = 0.100.$$

(a) How far can the spring be stretched without moving the mass? (b) If the object is set into oscillation with an amplitude twice the distance found in part (a), and the kinetic coefficient of friction is

$$μ_k = 0.0850,$$

what total distance does it travel before stopping? Assume it starts at the maximum amplitude.

You are looking to buy a small piece of land in Hong Kong. The price is "only" $\$ 60,000$ per square meter. The land title says the dimensions are $20 \mathrm{~m} \times 30 \mathrm{~m}$. By how much would the total price change if you measured the parcel with a steel tape measure on a day when the temperature was $20^{\circ} \mathrm{C}$ above the temperature that the tape measure was designed for? The dimensions of the land do not change.

How large an expansion gap should be left between steel railroad rails if they may reach a maximum temperature $35.0^{\circ} \mathrm{C}$ greater than when they were laid? Their original length is $10.0 \mathrm{~m}$.

What is the change in length of a $3.00 \mathrm{~cm}$ long column of mercury if its temperature changes from $37.0^{\circ} \mathrm{C}$ to $40.0^{\circ} \mathrm{C}$, assuming the mercury is constrained to a cylinder but unconstrained in length? Your answer will show why thermometers contain bulbs at the bottom instead of simple columns of liquid.

How much taller does the Eiffel Tower become at the end of a day when the temperature has increased by $15^{\circ} \mathrm{C}$ ? Its original height is $321 \mathrm{~m}$ and you can assume it is made of steel.

Find the area of the region described. shared by the circle r = 2 and the cardioid r = 2(1 - cos θ)

The height of the Washington Monument is measured to be $170.00 \mathrm{~m}$ on a day when the temperature is $35.0^{\circ} \mathrm{C}$. What will its height be on a day when the temperature falls to $-10.0^{\circ} \mathrm{C}$ ? Although the monument is made of limestone, assume that its coefficient of thermal expansion is the same as that of marble. Give your answer to five significant figures.

An ideal gas expands quasi-statically to three times its original volume. Which process requires more work from the gas, an isothermal process or an isobaric one? Determine the ratio of the work done in these processes.