Question: A cello string has a fundamental frequency

> (a) Show that since the bulk modulus has SI units N/m2 and mass density has SI units kg/m3, Eq. (12-1) gives the speed of sound in m/s. Thus, the equation is dimensionally consistent. (b) Show that no other combination of B and ρ can give dimensions of

> Two blocks lie side by side on a frictionless table. The block on the left is of mass m; the one on the right is of mass 2m. The block on the right is pushed to the left with a force of magnitude F, pushing the other block in turn. What force does the bl

> Someone steps on your toe, exerting a force of 500 N on an area of 1.0 cm2. What is the average pressure on that area in atm?

> A tire with an inner volume of 0.0250 m3 is filled with air at a gauge pressure of 36.0 lb/in2. If the tire valve is opened to the atmosphere, what volume outside of the tire does the escaping air occupy? Some air remains within the tire occupying the or

> During a rehearsal, all eight members of the first violin section of an orchestra play a very soft passage. The sound intensity level at a certain point in the concert hall is 38.0 dB. What is the sound intensity level at the same point if only one of th

> A cylinder in a car engine takes Vi = 4.50 × 10−2 m3 of air into the chamber at 30°C and at atmospheric pressure. The piston then compresses the air to one-ninth of the original volume (0.111 Vi) and to 20.0 times the original pressure (20.0 Pi). What is

> When playing fortissimo (very loudly), a trumpet emits sound energy at a rate of 0.800 W out of a bell (opening) of diameter 12.7 cm. (a) What is the sound intensity level right in front of the trumpet? (b) If the trumpet radiates sound waves uniformly

> A flight attendant wants to change the temperature of the air in the cabin from 18.0°C to 21.0°C without changing the pressure. What fractional change in the number of moles of air in the cabin would be required?

> According to a treasure map, a treasure lies at a depth of 40.0 fathoms on the ocean floor due east from the lighthouse. The treasure hunters use sonar to find where the depth is 40.0 fathoms as they head east from the lighthouse. What is the elapsed tim

> Sand is composed of SiO2. Find the order of magnitude of the number of silicon (Si) atoms in a grain of sand. Approximate the sand grain as a sphere of diameter 0.5 mm and an SiO2 molecule as a sphere of diameter 0.5 nm.

> Horseshoe bats use the Doppler effect to determine their location. A Horseshoe bat flies toward a wall at a speed of 15 m/s while emitting a sound of frequency 35 kHz. What is the beat frequency between the emission frequency and the echo?

> At 0.0°C and 1.00 atm, 1.00 mol of a gas occupies a volume of 0.0224 m3. (a) What is the number density? (b) Estimate the average distance between the molecules. (c) If the gas is nitrogen (N2), the principal component of air, what is the total mass a

> The orange jewelweed (Impatiens capensis) has seed pods that explode when lightly touched, launching the seeds as projectiles to disperse them. Suppose a seed is launched at 1.2 m/s from a height of 1.1 m. Assume air resistance is negligible and that the

> A bicycle has wheels of radius 0.32 m. Each wheel has a rotational inertia of 0.080 kg·m2 about its axle. The total mass of the bicycle including the wheels and the rider is 79 kg. When coasting at constant speed, what fraction of the total kinetic energ

> A jetliner flies east for 600.0 km, then turns 30.0° toward the south and flies another 300.0 km. (a) How far is the plane from its starting point? (b) In what direction could the jetliner have flown directly to the same destination (in a straight-line

> Bats of the Vespertilionidae family detect the distance to an object by timing how long it takes for an emitted signal to reflect off the object and return. Typically they emit sound pulses 3 ms long and 70 ms apart while cruising. (a) If an echo is hea

> (a) In Problem 49, find the beat frequency between the outgoing and reflected sound waves. (b) Show that the beat frequency is proportional to the speed of the blood cell if v ≪ u. [Hint: Use the binomial approximation from Appendix A.9.]

> A sound wave arriving at your ear is transferred to the fluid in the cochlea. If the intensity in the fluid is 0.80 times that in air and the frequency is the same as for the wave in air, what will be the ratio of the pressure amplitude of the wave in ai

> Doppler ultrasound is used to measure the speed of blood flow (see Problem 49). The reflected sound interferes with the emitted sound, producing beats. If the speed of red blood cells is 0.10 m/s, the ultrasound frequency used is 5.0 MHz, and the speed o

> Scuba divers are admonished not to rise faster than their air bubbles when rising to the surface. This rule helps them avoid the rapid pressure changes that cause the “bends.” Air bubbles of 1.0 mm radius are rising from a scuba diver to the surface of t

> The bat of Problem 55 emits a chirp that lasts for 2.0 ms and then is silent while it listens for the echo. If the beginning of the echo returns just after the outgoing chirp is finished, how close to the moth is the bat? [Hint: Is the change in distance

> In an aortic aneurysm, a bulge forms where the walls of the aorta are weakened. If blood flowing through the aorta (radius 1.0 cm) enters an aneurysm with a radius of 3.0 cm, how much on average is the blood pressure higher inside the aneurysm than the p

> A bat emits chirping sounds of frequency 82.0 kHz while hunting for moths to eat. If the bat is flying toward the moth at a speed of 4.40 m/s and the moth is flying away from the bat at 1.20 m/s, what is the frequency of the sound wave reflected from the

> If the cardiac output of a small dog is 4.1 × 10−5 m3/s, the radius of its aorta is 0.50 cm, and the aorta length is 40.0 cm, determine the pressure drop across the aorta of the dog. Assume the viscosity of blood is 4.0 × 10−3 Pa·s.

> Find the ratio of the rotational inertia of Earth for rotation about its own axis to its rotational inertia for revolution about the Sun.

> A ship mapping the depth of the ocean emits a sound of 38 kHz. The sound travels to the ocean floor and returns 0.68 s later. (a) How deep is the water at that location? (b) What is the wavelength of the wave in water? (c) What is the wavelength of th

> 100. At 3:00 P.M., a bank robber is spotted driving north on I-15 at milepost 126. His speed is 112.0 mi/h. At 3:37 P.M., he is spotted at milepost 185 doing 105.0 mi/h. During this time interval, what are the bank robber’s displacement, average velocity

> Two children ride on a merry-go-round. One is 2 m from the axis of rotation and the other is 4 m from it. Which child has the larger (a) linear speed, (b) acceleration, (c) angular speed, and (d) angular displacement?

> If you watch water falling from a faucet, you will notice that the flow decreases in radius as the water falls. This can be explained by the equation of continuity, since the cross-sectional area of the water decreases as the speed increases. If the wate

> A ship is lost in a dense fog in a Norwegian fjord that is 1.80 km wide. The air temperature is 5.0°C. The captain fires a pistol and hears the first echo after 4.0 s. (a) How far from one side of the fjord is the ship? (b) How long after the first ech

> Near sea level, how high a hill must you ascend for the reading of a barometer you are carrying to drop by 10 mmHg? Assume the temperature remains at 20°C as you climb. The reading of a barometer on an average day at sea level is 760 mmHg.

> The pitch of the sound from a race car engine drops the musical interval of a fourth when it passes the spectators. This means the frequency of the sound after passing is 0.75 times what it was before. How fast is the race car moving?

> The body of a 90.0 kg person contains 0.020 m3 of body fat. If the density of fat is 890 kg/m3, what percentage of the person’s body weight is composed of fat?

> Blood flow rates can be found by measuring the Doppler shift in frequency of ultrasound reflected by red blood cells (known as angiodynography). If the speed of the red blood cells is v, the speed of sound in blood is u, the ultrasound source emits waves

> The pressure in a water pipe in the basement of an apartment house is 4.10 × 105 Pa, but on the seventh floor it is only 1.85 × 105 Pa. What is the height between the basement and the seventh floor? Assume the water is not flowing; no faucets are opened.

> A 62 kg woman takes 6.0 s to run up a flight of stairs. The landing at the top of the stairs is 5.0 m above her starting place. (a) What is the woman’s average power output while she is running? (b) Would that be equal to her average power input—the ra

> A source and an observer are each traveling at 0.50 times the speed of sound. The source emits sound waves at 1.0 kHz. Find the observed frequency if (a) the source and observer are moving toward each other; (b) the source and observer are moving away

> The deepest place in the ocean is the Marianas Trench in the western Pacific Ocean, which is over 11.0 km deep. On January 23, 1960, the research sub Trieste went to a depth of 10.915 km, nearly to the bottom of the trench. This still is the deepest dive

> Fish don’t move as fast as you might think. A small trout has a top swimming speed of only about 2 m/s, which is about the speed of a brisk walk (for a human, not a fish!). It may seem to move faster because it is capable of large accelerations—it can da

> A speedboat is traveling at 20.1 m/s toward another boat moving in the opposite direction with a speed of 15.6 m/s. The speedboat pilot sounds his horn, which has a frequency of 312 Hz. What is the frequency heard by a passenger in the oncoming boat?

> An 1100 kg airplane starts from rest and accelerates horizontally forward for 8.0 s until it reaches its takeoff speed of 35 m/s. What is the average net force on the airplane during this time?

> An atomizer is a device that delivers a fine mist of some liquid such as perfume by blowing air horizontally over the top of a tube immersed in the liquid. Suppose a perfume with density 800 kg/m3 has a 3.0 cm tube extending vertically from the top of th

> In parts of the midwestern United States, sirens sound when a severe storm that may produce a tornado is approaching. Mandy is walking at a speed of 1.56 m/s directly toward one siren and directly away from another siren when they both begin to sound wit

> A very large vat of water has a hole 1.00 cm in diameter located a distance 1.80 m below the water level. (a) How fast does water exit the hole? (b) How would your answer differ if the vat were filled with gasoline? (c) How would your answer differ if

> At a factory, a noon whistle is sounding with a frequency of 500 Hz. As a car traveling at 85 km/h approaches the factory, the driver hears the whistle at frequency fi. After driving past the factory, the driver hears frequency ff. What is the change in

> Two identical beakers are filled to the brim and placed on balance scales. The base area of the beakers is large enough that any water that spills out of the beakers will fall onto the table the scales are resting on. A block of pine (density = 420 kg/m3

> How much work is done by the motor in a CD player to make a CD spin, starting from rest? The CD has a diameter of 12.0 cm and a mass of 15.8 g. The laser scans at a constant tangential velocity of 1.20 m/s. Assume that the music is first detected at a ra

> An ambulance traveling at 44 m/s approaches a car heading in the same direction at a speed of 28 m/s. The ambulance driver has a siren sounding at 550 Hz. At what frequency does the driver of the car hear the siren?

> A 85.0 kg canoe made of thin aluminum has the shape of half of a hollowed-out log with a radius of 0.475 m and a length of 3.23 m. (a) When this is placed in the water, what percentage of the volume of the canoe is below the waterline? (b) How much add

> (a) If a freestyle swimmer travels 1.50 km in a time of 14 min 53 s, how fast is his average speed? (b) If the pool is rectangular and 50 m in length, how does the speed you found compare with his sustained swimming speed of 1.54 m/s during one length o

> A block of aluminum that has dimensions 2.00 cm by 3.00 cm by 5.00 cm is suspended by a thread from a spring scale. (a) What is the scale reading in grams? (b) A beaker full of oil (density 850 kg/m3) rests on a second scale, which reads 460.0 g. The b

> A musician plays a string on a guitar that has a fundamental frequency of 330.0 Hz. The string is 65.5 cm long and has a mass of 0.300 g. (a) At what speed do the waves travel on the string? (b) What is the tension in the string? (c) While the guitar

> A bridal party is at a rehearsal dinner. The best man challenges the bridegroom to pick up an olive using only a brandy snifter. How does the groom accomplish this task?

> A section of pipe with an internal diameter of 10.0 cm tapers to an inner diameter of 6.00 cm as it rises through a height of 1.70 m at an angle of 60.0° with respect to the horizontal. The pipe carries water and its higher end is open to air. (a) If th

> An auditorium has organ pipes at the front and at the rear of the hall. Two identical pipes, one at the front and one at the back, have fundamental frequencies of 264.0 Hz at 20.0°C. During a performance, the organ pipes at the back of the hall are at 25

> A beach ball is thrown straight up in the air. The graph shows its vertical velocity component as a function of time. The dashed line is tangent to the curve at the point where vy = 0. (a) What shape would the vy(t) graph have if air drag on the beach b

> Calculate the rotational inertia for each of the three arrangements.

> A piano tuner sounds two strings simultaneously. One has been previously tuned to vibrate at 293.0 Hz. The tuner hears 3.0 beats per second. The tuner increases the tension on the as-yet untuned string, and now when they are played together the beat freq

> A cube that is 4.00 cm on a side and of density 8.00 × 102 kg/m3 is attached to one end of a spring. The other end of the spring is attached to the base of a beaker. When the beaker is filled with water until the entire cube is submerged, the spring is s

> (a) What is the energy of a pendulum (L = 1.0 m, m = 0.50 kg) oscillating with an amplitude of 5.0 cm? (b) The pendulum’s energy loss (due to damping) is replaced in a clock by allowing a 2.0 kg mass to drop 1.0 m in 1 week. What average percentage of t

> The potential energy associated with surface tension is much like the elastic potential energy of a stretched spring or a balloon. Suppose we do work on a puddle of liquid, spreading it out through a distance of As along a line L perpendicular to the for

> In a playground, two slides have different angles of incline θ1 and θ2 (θ2 > θ1) A child slides down the first at constant speed; on the second, his acceleration down the slide is a. Assume the coefficient of kinetic friction is the same for both slides.

> A pendulum of length 120 cm swings with an amplitude of 2.0 cm. Its mechanical energy is 5.0 mJ. What is the mechanical energy of the same pendulum when it swings with an amplitude of 3.0 cm?

> A dinoflagellate takes 5.0 s to travel 1.0 mm. Approximate a dinoflagellate as a sphere of radius 35.0 μm (ignoring the flagellum). (a) What is the drag force on the dinoflagellate in seawater of viscosity 0.0010 Pa·s? (b) What is the power output of th

> Christy has a grandfather clock with a pendulum that is 1.000 m long. (a) If the pendulum is modeled as a simple pendulum, what would be the period? (b) Christy observes the actual period of the clock, and finds that it is 1.00% faster than that for a

> Sketch a graph of ax(t) for the car in Problem 43.

> Show that the charge of the neutron and the charge of the proton are consistent with their constituent quark content.

> An owl has good night vision because its eyes can detect a light intensity as faint as 5.0 × 10−13 W/m2. What is the minimum number of photons per second that an owl eye can detect if its pupil has a diameter of 8.5 mm and the light has a wavelength of 5

> Depressing the brake pedal in a car pushes on a piston with cross- sectional area 3.0 cm2. The piston applies pressure to the brake fluid, which is connected to two pistons, each with area 12.0 cm2. Each of these pistons presses a brake pad against one s

> The pendulum for a grandfather clock consists of a thin rigid rod (of negligible mass) with two metal disks attached to it. One disk has mass 0.600 kg and is attached to the rod 0.800 m from the pivot; the other has mass 0.750 kg and is attached 1.20 m f

> A hydraulic lift is lifting a car that weighs 12 kN. The area of the piston supporting the car is A, the area of the other piston is a, and the ratio A/a is 100.0. How far must the small piston be pushed down to raise the car a distance of 1.0 cm? [Hint:

> Max’s arm weighs 34 N and is 63 cm long. If Max lets his relaxed arm swing back and forth like a pendulum, what is the period? Model the arm as a uniform rod.

> The pressure inside a bottle of champagne is 4.5 atm higher than the air pressure outside. The neck of the bottle has an inner radius of 1.0 cm. (a) What is the frictional force on the cork due to the neck of the bottle? (b) The cork (mass 7.5 g) is lo

> Marie slides a paper plate with a slice of pizza across a horizontal table to her friend Jaden. The coefficient of friction between the table and plate is 0.32. If the pizza must travel 44 cm to get from Marie to Jaden, what initial speed should Marie gi

> A grandfather clock is constructed so that it has a simple pendulum that swings from one side to the other, a distance of 20.0 mm, in 1.00 s. What is the maximum speed of the pendulum bob? Use two different methods. First, assume SHM and use the relation

> Water enters an apartment building 0.90 m below the street level with a gauge pressure of 52.0 kPa through the main pipe, which has a 5.00 cm radius. A second-story bathroom has an open faucet with a 1.20 cm radius that is located 4.20 m above the street

> A pendulum clock has a period of 0.650 s on Earth. It is taken to another planet and found to have a period of 0.862 s. The change in the pendulum’s length is negligible. (a) Is the gravitational field strength on the other planet greater than or less t

> Atmospheric pressure is equal to the weight of a vertical column of air, extending all the way up through the atmosphere, divided by the cross-sectional area of the column. (a) Explain why that must be true. [Hint: Apply Newton’s second law to the colum

> If the skier of Example 6.6 is moving at 12 m/s at the bottom of the trail, calculate the total work done by friction and air resistance during the run. The skier’s mass is 75 kg.

> A pendulum (mass m) moves according to x = A sin ωt. (a) Write the equation for vx(t) and sketch one cycle of the vx(t) graph. (b) What is the maximum kinetic energy?

> A physics teacher draws a cutaway view of a car rounding a banked curve as a rectangle atop a right triangle. A student draws a coordinate system on the drawing. Is there another choice of axes that would make the problem easier to solve?

> A U-shaped tube is partly filled with water and partly filled with a liquid that does not mix with water. Both sides of the tube are open to the atmosphere. What is the density of the liquid (in g/cm3)?

> Each of five pendulums has a bob of mass m suspended from a string of length L. Rank them in order of their frequency for small- amplitude oscillations, greatest to smallest. (a) m = 300 g, L = 1.10 m (b) m = 330 g, L = 1.10 m (c) m = 330 g, L = 1.00 m

> To measure the airspeed of a plane, a device called a Pitot tube is used. A simplified model of the Pitot tube is a manometer with one side connected to a tube facing directly into the “wind” (stopping the air that hit

> A pendulum of length 75 cm and mass 2.5 kg swings with a mechanical energy of 0.015 J. What is the amplitude?

> A pellet is fired from a toy cannon with a velocity of 12 m/s directed 60° above the horizontal. After 0.10 s, a second pellet is fired with the same initial velocity. After an additional 0.15 s have passed, what is the velocity of the first pellet with

> Refer to Problems 11–14. Find the final speed of the sliding crate if the frictional force on the sliding crate has magnitude 19.4 N.

> On a nice day when the temperature outside is 20°C, you take the elevator to the top of the Willis Tower in Chicago, which is 440 m tall. (a) How much less is the air pressure at the top than the air pressure at the bottom? Express your answer both in P

> Are evenly spaced specific-gravity markings on the cylinder of a hydrometer equal distances apart? In other words, is the depth d to which the cylinder is submerged linearly related to the density ρ of the fluid? To answer this question, assume that the

> Rank the three arrangements in increasing order of the rotational inertia.

> What is the period of a pendulum consisting of a 6.0 kg mass hanging from a 4.0 m long string?

> Suppose the hydrometer has a cylindrical stem of cross-sectional area 0.400 cm2. The total volume of the bulb and stem is 8.80 cm3, and the mass of the hydrometer is 4.80 g. (a) How far from the top of the cylinder should a mark be placed to indicate a

> A 230.0 g object on a spring oscillates on a frictionless horizontal surface with frequency 2.00 Hz and amplitude 8.00 cm. Its position as a function of time is given by x = A sin ωt. (a) Sketch a graph of the elastic potential energy as a function of t

> A block of wood, with density 780 kg/m3, has a cubic shape with sides 0.330 m long. A cord of negligible mass is used to tie a piece of lead to the bottom of the wood. The lead pulls the wood into the water until it is just completely covered with water.

> A ball is dropped from a height h onto the floor and keeps bouncing. No energy is dissipated, so the ball regains the original height h after each bounce. Sketch the graph for y(t) and list several features of the graph that indicate that this motion is

> The figure shows a plot of vx(t) for a car traveling in a straight line. (a) What is aav,x between t = 6 s and t = 11 s? (b) What is vav,x for the same time interval? (c) What is vav,x for the interval t = 0 to t = 20 s? (d) What is the increase in the

> A plastic beach ball has radius 20.0 cm and mass 0.10 kg, not including the air inside. (a) What is the weight of the beach ball including the air inside? Assume the air density is 1.3 kg/m3 both inside and outside. (b) What is the buoyant force on the

> An object is attached to an ideal spring of spring constant 2.5 N/m. The spring is initially in its relaxed position. The object is then released and oscillates about its equilibrium position. The motion is described by What is the maximum kinetic energy

> A stone of weight W has specific gravity 2.50. (a) When the stone is suspended from a scale and submerged in water, what is the scale reading in terms of its weight in air? (b) What is the scale reading for the stone when it is submerged in oil (specif

> A gull is flying horizontally 8.00 m above the ground at 6.00 m/s. The bird is carrying a clam in its beak and plans to crack the clamshell by dropping it on some rocks below. Ignoring air resistance, (a) what is the horizontal distance to the rocks at