A hummingbird in flight beats its wings at a rate of 70 times per second. How many times does it beat its wings in an hour if it is in flight 70% of the time?

Two tuning forks are producing sounds of wavelength $34.40 \mathrm{~cm}$ and $33.94 \mathrm{~cm}$ simultaneously. How many beats do you hear each second?

A typical person has a heart rate of $70$ beats per minute and takes 12 breaths in a minute. Show that her heart beats about $4200$ times an hour, 100,800 times a day, and $36.8$ million times a year. Show also that she takes about $720$ breaths per hour, $17,280$ breaths per day, and $6.3$ million breaths per year.

"To tune your violin, you first tune the A string to the correct pitch of $440 \text{~Hz}$, and then you bow both it and an adjoining string simultaneously, all the while listening for beats. While bowing the A and E strings, you hear a beat frequency of $3.00 \text{~Hz}$ and note that the beat frequency increases as the tension on the E string are increased. (The E string is to be tuned to $660 \text{~Hz}$.) $(a)$ Why are beats produced by these two strings when bowed simultaneously?"

If h(t) is a person's heart rate in beats per minute t minutes into an exercise session, what does

$$\int_{0}^{30} h(t) d t$$

represent?

Imagine that you and a friend are trying to tune the lowest strings on two different guitars to the same pitch. Explain how you could use beats to determine if the strings are tuned to the same frequency.

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.

Why do you think Neruda calls the "constancy that beats in your chest" (literally, his beloved's heartbeat) a "purer motion"? Interpret the remarkable visual image in line $11$.

A lion's heart beats 12 times in 16 s. How many times does a lion's heart beat in 60 s?

$$F. \ 24 \\ G. \ 32 \\ H. \ 45 \\ J. \ 192$$

The blue-throated hummingbird has a heart rate of about 1,260 beats per minute. Explain how you would calculate the number of times the hummingbird's heart beats in a 24-hour day. Then find the number of beats in a 24-hour day.

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?

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?

Five pulse rates randomly selected and have a mean of 78.0 beats per minute. Four of the pulse rates are 82, 78, 56, and 84.Find the mis ing value.

(II) A source emits sound of wavelengths $2.64 \mathrm{~m}$ and $2.72 \mathrm{~m}$ in air. (a) How many beats per second will be heard? (Assume $T=20^{\circ} \mathrm{C}$.)