You are working at an open-air amphitheater, where rock concerts occur regularly. The venue has powerful loudspeakers mounted on 10.6-m-tall columns at various locations surrounding the audience. The loudspeakers emit sound uniformly in all directions. There are ladder steps sticking out from the columns, to help workers service the loudspeakers. Many times, audience members break through the protective fencing around the columns and climb upward on the columns to get a better view of the performers. The upcoming concert is by a group that states that several very-high-volume pulses of sound occur in their concerts, and these sounds are part of their artistic expression. The amphitheater owners are worried about people climbing the columns and being too close to the loudspeakers when these peak sounds are emitted. They do not want to be held responsible for injuries to audience members' ears. Based on past performances of the group, you determine that the peak sound level is 150 dB measured 20.0 cm from the speakers on the columns. The owners ask you to determine the heights on the columns at which to mount impassable barricades to keep people from getting too close to the speakers and hearing sound above the threshold of pain.

Tension is maintained in a string. The observed wave speed is v = 24.0 m/s when the suspended mass is m = 3.00 kg. (a) What is the mass per unit length of the string? (b) What is the wave speed when the suspended mass is m = 2.00 kg?

Complete the table and use the result to estimate the limit. Use a graphing utility to graph the function to confirm your result. $\lim _{x \rightarrow-4} \frac{\frac{1}{x+4}-\frac{1}{4}}{x}$

$$\begin{matrix} \text{x} & \text{-4.1} & \text{-4.01} & \text{-4.001} & \text{-4}\\ \text{f(x)} & \text{?}\\ \end{matrix}$$

In a darkened room, a burning candle is placed 1.50 m from a white wall. A lens is placed between the candle and the wall at a location that causes a larger, inverted image to form on the wall. When the lens is in this position, the object distance is $p_{1}$. When the lens is moved 90.0 cm toward the wall, another image of the candle is formed on the wall. From this information, we wish to find $p_{1}$ and the focal length of the lens. (a) From the lens equation for the first position of the lens, write an equation relating the focal length f of the lens to the object distance $p_{1},$ with no other variables in the equation. (b) From the lens equation for the second position of the lens, write another equation relating the focal length f of the lens to the object distance $p_{1}$. (c) Solve the equations in parts (a) and (b) simultaneously to find $p_{1}$ (d) Use the value in part (c) to find the focal length f of the lens.

An experimenter wishes to generate in air a sound wave that has a displacement amplitude of $5.50 \times 10–6$ m. The pressure amplitude is to be limited to 0.840 Pa. What is the minimum wavelength the sound wave can have?

Table 2 shows the rates for natural gas charged by the Middle Tennessee Natural Gas Utility District during winter months. The base charge is a fixed monthly charge, independent of the amount of gas used per month.

$$\begin{matrix} \text{Base charge} & \text{}{\$ 5.00}\\ \text{First 5 therms} & \text{0.69 per therm}\\ \text{Next 45 therms} & \text{0.65 per therm}\\ \text{Over 50 therms} & \text{0.63 per therm}\\ \end{matrix}$$

(A) Write a piecewise definition of the monthly charge S(x) for a customer who uses x therms in a winter month. (B) Graph S(x). (C) Is S(x) continuous at x=5? At x=50? Explain.

Solve each equation. $|4 x+3|=7$

Transverse waves are being generated on a rope under constant tension. By what factor is the required power increased or decreased if (a) the length of the rope is doubled and the angular frequency remains constant, (b) the amplitude is doubled and the angular frequency is halved, (c) both the wavelength and the amplitude are doubled, and (d) both the length of the rope and the wavelength are halved?

What are organization expenses? Provide examples.

Read these two sentences from the passage: “How, in the vast ocean, did a handful of new molecules and compounds get together to form the more complex chemicals that led to life? That’s the question Hazen is working on now.” Which of the following describes the relationship between these two sentences? 1. The sentences make a comparison. 2. The sentences argue about a topic. 3. The second sentence adds information to the first sentence. 4. The second sentence shows the effect of the first sentence.

The speed of sound in air (in meters per second) depends on temperature according to the approximate expression $v=331.5+0.607 T_{\mathrm{C}}$ where $T_{\mathrm{C}}$ is the Celsius temperature. In dry air, the temperature decreases about $1^{\circ} \mathrm{C}$ for every 150-m rise in altitude. (a) Assume this change is constant up to an altitude of 9000 m. What time interval is required for the sound from an airplane flying at 9000 m to reach the ground on a day when the ground temperature is $30^{\circ} \mathrm{C} ?$ (b) What If? Compare your answer with the time interval required if the air were uniformly at $30^{\circ} \mathrm{C}.$ Which time interval is longer?

Summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of y=f(x). $f(x)=\frac{-5 x}{(x-1)^{2}}$

A sinusoidal sound wave moves through a medium and is described by the displacement wave functionwhere s is in micrometers, x is in meters, and t is in seconds. Find (a) the amplitude, (b) the wavelength, and (c) the speed of this wave. (d) Determine the instantaneous displacement from equilibrium of the elements of the medium at the position x = 0.050 0 m at t = 3.00 ms. (e) Determine the maximum speed of the element’s oscillatory motion. $s ( x , t ) = 2.00 \cos ( 15.7 x - 858 t )$

Consider an infinite number of identical particles, each with charge q, placed along the x axis at distances a, 2a, 3a, 4a, $\ldots$ from the origin. What is the electric field at the origin due to this distribution? Suggestion: Use

$$1+\frac{1}{2^{2}}+\frac{1}{3^{2}}+\frac{1}{4^{2}}+\dots=\frac{\pi^{2}}{6}$$