A police siren contains at least two frequencies, producing the wavering sound (beats). Explain how the siren sound changes as a police car approaches, passes, and moves away from a pedestrian.

A classic demonstration of the physics of sound involves an alarm clock in a bell vacuum jar. The demonstration starts with air in the vacuum jar at normal atmospheric pressure and then the jar is evacuated to lower and lower pressures. Describe the expected outcome.

A (somewhat risky) way of telling if a train that cannot be seen or heard is approaching is by placing your ear on the rail. Explain why this works.

Three physics faculty members sit in three different cars at a railroad crossing. Three trains go by at different (constant) speeds, each emitting the same sound. Each faculty member uses a cell phone to record the sound of a different train. On the next day, during a faculty meeting, they plot the frequency as a function of time on a computer, which of the three faculty members was closest to the train tracks? a) the one who recorded the sound represented by the solid line b) the one who recorded the sound represented by the dashed line c) the one who recorded the sound represented by the dotted line d) impossible to tell

You stand on the curb waiting to cross a street. Suddenly you hear the sound of a horn from a car approaching you at a constant speed. You hear a frequency of $80 \mathrm{~Hz}$. After the car passes by, you hear a frequency of $72 \mathrm{~Hz}$. At what speed was the car traveling? a) $17 \mathrm{~m} / \mathrm{s}$ b) $18 \mathrm{~m} / \mathrm{s}$ c) $19 \mathrm{~m} / \mathrm{s}$ d) $20 \mathrm{~m} / \mathrm{s}$

Find mean, median, mode, and range. Which measure best describes each group of data? Explain. resting heart rate in beats per minute: 79 72 80 81 40 72

To play a $\mathrm{C}$ major chord on the piano, you hit the $\mathrm{C}, \mathrm{E}$, and $\mathrm{G}$ keys simultaneously. When you do so, you hear no beats. Why?

Use a case $1$-case $2$ ratio box to solve this problem. Don's heart beats $225$ times in $3$ minutes. At that rate, how many times will his heart beat in $5$ minutes?

The hummingbird has an average wing speed of $70$ beats per second. The expression $70 t$ gives the number of wingbeats in $t$ seconds.

Calculate the number of wingbeats in 1 hour for the hummingbird.

In 20 minutes, how many more times does a gerbil's heart beat than a rabbit's?

A $2.00 \mathrm{MHz}$ sound wave travels through a pregnant woman's abdomen and is reflected from the fetal heart wall of her unborn baby. The heart wall is moving toward the sound receiver as the heart beats. The reflected sound is then mixed with the transmitted sound, and $85$ beats per second are detected. The speed of sound in body tissue is $1500 \mathrm{~m} / \mathrm{s}$. Calculate the speed of the fetal heart wall at the instant this measurement is made.

Show that in a tournament (defined preceding mentioned theorem) it is always possible to rank the contestants so that the person ranked ith beats the person ranked (i +1)st. (Hint: Use the mentioned theorem.)

A tuning fork is known to vibrate with frequency $262 \mathrm{~Hz}$. When it is sounded along with a mandolin string, four beats are heard every second. Next, a bit of tape is put onto each tine of the tuning fork, and the tuning fork now produces five beats per second with the same mandolin string. What is the frequency of the string?
(a) $257 \mathrm{~Hz}$
(b) $258 \mathrm{~Hz}$
(c) $262 \mathrm{~Hz}$
(d) $266 \mathrm{~Hz}$
(e) $267 \mathrm{~Hz}$
(f) This sequence of events could not happen.

Recommended heart rates during exercise vary with age and physical condition. For a healthy person doing moderate to intense exercise, such as hiking, the inequality $0.5(220-a) \leq R \leq 0.9(220-a)$ gives a target range for the heart rate R (in beats per minute), based on age a (in years). a. What is the target range for heart rates for a person 15 years old? b. How old is a person whose target range is between 99 and 178.2 beats per minute?