You have two steel strings of equal length under equal tension. If they're to vibrate with fundamental frequencies exactly one octave apart, what should be the ratio of the strings' diameters?

Sometimes, even with a wrench, one cannot loosen a nut that is frozen tightly to a bolt. It is often possible to loosen the nut by slipping one end of a long pipe over the wrench handle and pushing at the other end of the pipe. With the aid of the pipe, does the applied force produce a smaller torque, a greater torque, or the same torque on the nut?

A merry-go-round at a playground is a circular platform that is mounted parallel to the ground and can rotate about an axis that is perpendicular to the platform at its center. The angular speed of the merry-go-round is constant, and a child at a distance of 1.4 m from the axis has a tangential speed of 2.2 m/s. What is the tangential speed of another child, who is located at a distance of 2.1 m from the axis? (a) 1.5 m/s (b) 3.3 m/s (c) 2.2 m/s (d) 5.0 m/s (e) 0.98 m/s

A space probe is traveling in outer space with a momentum that has a magnitude of

$$7.5 \times 10 ^ { 7 } \mathrm { kg } \cdot \mathrm { m } / \mathrm { s }.$$

A retrorocket is fired to slow down the probe. It applies a force to the probe that has a magnitude of

$$2.0 \times 10 ^ { 6 } \mathrm { N }$$

and a direction opposite to the probe's motion. It fires for a period of 12 s. Determine the momentum of the probe after the retrorocket ceases to fire

A volleyball is spiked so that its incoming velocity of +4. 0 m/s is changed to an outgoing velocity of -21 m/s. The mass of the volleyball is 0.35 kg. What impulse does the player apply to the ball?

A crude model of the human vocal tract treats it as a pipe closed at one end. Find the effective length of the vocal tract in a person whose fundamental tone is $620 \mathrm{~Hz}$. Assume air at body temperature. Note: Variations in the shape of the mouth and position of the tongue significantly alter this simple model.

A piano's A string $(f=440 \mathrm{~Hz})$ is $38.9 \mathrm{~cm}$ long and clamped at both ends. If the string is under $667 \mathrm{~N}$ tension, what's its mass?

A bat emits a $52.0-\mathrm{kHz}$ ultrasound burst as it flies toward a cave wall at $7.50 \mathrm{~m} / \mathrm{s}$. At what frequency does the bat receive the reflected pulse? Hint: Consider the Doppler-shifted frequency of the emitted waves striking the wall and then a second Doppler shift of the reflected pulse received by the bat. Assume air at $20^{\circ} \mathrm{C}$.

A 1.12-m-long organ pipe has one end open. Among its possible standing-wave frequencies is $225 \mathrm{~Hz}$. The next higher frequency is $375 \mathrm{~Hz}$. Do not assume that the speed of sound is $343 \mathrm{~m} / \mathrm{s}$. Find (b) the sound speed.

A 1.12-m-long organ pipe has one end open. Among its possible standing-wave frequencies is $225 \mathrm{~Hz}$. The next higher frequency is $375 \mathrm{~Hz}$. Do not assume that the speed of sound is $343 \mathrm{~m} / \mathrm{s}$. Find (a) the fundamental frequency.

Having grown tired of hearing loud music from passing cars at 3 AM and the boisterous yelling of bar patrons at closing, a professor buys a new home in a quiet neighborhood. She is, however, concerned about noise from freeway traffic. Using a sound intensity level meter, she stands at an overpass $10 \mathrm{~m}$ above the passing cars and measures a maximum intensity level of $80 \mathrm{~dB}$. If her new home is $2.6 \mathrm{~km}$ from the freeway, what's the intensity level there? Assume no decrease due to absorption by air, trees, or other objects. Compare your result with a quiet whisper, $20 \mathrm{~dB}$.

You're directly between two louds peakers emitting $720-\mathrm{Hz}$ tones. How fast would you have to walk or run on a direct line between the speakers to hear a difference of $2.0 \mathrm{~Hz}$ between the two tones?

Suppose you double your original distance from a sound source. (b) By how many decibels does the intensity level decrease?

Suppose you double your original distance from a sound source. (a) By what factor does the sound intensity decrease?