A sound wave of frequency 300 Hz has an intensity of 1.00 μW/m². What is the amplitude of the air oscillations caused by this wave?

When the door of the Chapel of the Mausoleum in Hamilton, Scotland, is slammed shut, the last echo heard by someone standing just inside the door reportedly comes 15 s later. If that echo were due to a single reflection off a wall opposite the door, how far from the door is the wall?

The A string of a violin is a little too tightly stretched. Beats at 4.00 per second are heard when the string is sounded together with a tuning fork that is oscillating accurately at concert A (440 Hz). What is the period of the violin string oscillation?

The A string of a violin is a little too tightly stretched. Beats at 4.50 per second are heard when the string is sounded together with a tuning fork that is oscillating accurately at concert A (440 Hz). What is the period of the violin string oscillation?

Diagnostic ultrasound of frequency 4.50 MHz is used to examine tumors in soft tissue. What is the wavelength in air of such a sound wave?

Find the speed of waves on a violin string of mass 800 mg and length 22.0 cm if the fundamental frequency is 920 Hz.

An article in Hotwire (Dec. 2002) discussed the length of time till failure of a product produced at Hewlett-Packard. At the end of the product’s lifetime, the time till failure is modeled using an exponential distribution with mean 500 thousand hours. In reliability jargon, this is known as the “wear-out” distribution for the product. During its normal (useful) life, assume the product’s time till failure is uniformly distributed over the range 100 thousand to 1 million hours. a. At the end of the product’s lifetime, find the probability that the product fails before 700 thousand hours. b. During its normal (useful) life, find the probability that the product fails before 700 thousand hours. c. Show that the probability of the product failing before 830 thousand hours is approximately the same for both the normal (useful) life distribution and the wear-out distribution.

Use a statistical software package to generate 100 random samples of size n = 2 from a population characterized by a normal probability distribution with a mean of 100 and a standard deviation of 10. Compute

$$\overline { x }$$

for each sample, and plot a frequency distribution for the 100 values of

$$\overline { x }$$

Repeat this process for n = 5, 10, 30, and 50. How does the fact that the sampled population is normal affect the sampling distribution of

$$\overline { x } ?$$

Simplify:

$$(5p)^0 (5p)^1$$

Triangle ABC has coordinates A(1, 5), B(-2, 1), and C(-2, 4). Sketch triangle ABC and A'B'C for the dilation (x, y)

$$\rightarrow$$

(-2x, -2y). What is the effect of a negative scale factor?

Solve each equation on the interval

$$[ 0,2 \pi ).$$

Use exact values where possible or give approximate solutions correct to four decimal places.

$$\sin 2 x + \cos x = 0$$

An identity is an equation that is true for all the allowed values of the variable. Use what you know about trigonometric ratios to show that each equation is an identity.

$$\sin X = \cos X \cdot \tan X$$

A motorboat takes 40 minutes to travel 20 miles downstream. The return trip takes 60 minutes. What is the speed of the current?

Suppose that the sound level of a conversation is initially at an angry 70 dB and then drops to a soothing 50 dB. Assuming that the frequency of the sound is 500 Hz, determine the final sound intensities.