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

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?

"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?"

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.

(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 $T=20^{\circ} \mathrm{C}$.)

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?

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 $2.00 \mathrm{MHz}$ 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.

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?

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

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

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

Assuming the heart beats once every second, how many times does the heart beat in 1 year? How many times does it beat in 40 years? 70 years?

Applying Concepts 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.