# Standing Wave and Harmonic Motions

A tube of air is open at only one end and has a length of 1.5 m. This tube sustains a standing wave at its third harmonic. What is the distance between one node and the adjacent antinode?

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#### Solution Summary

This solution contains a diagram representing the harmonic motion of the air in the tube and contains step-by-step calculations to determine the distance between anode and an antinode.

Multiple choice questions related to wave mechanics, fluid dynamics, simple harmonic motion, gravitational filed, angular momentum and center of mass.

(See attached file for full problem description)

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An 82.0 kg-diver stands at the edge of a light 5.00-m diving board, which is supported by two pillars 1.60 m apart.

Find the force exerted by pillar B:

a. 1.71 kN downwards.

b. 1.71 kN upwards.

c. 2.51 kN downwards.

d. 2.51 kN upwards.

A meter stick balances at the 50.0-cm mark. If a mass of 50.0 g is placed at the 90.0-cm mark, the stick balances at the 61.3-cm mark. What is the mass of the meter stick?

a. 127 g

b. 178 g

c. 32.6 g

d. 73.4 g

A uniform meter stick with a mass of 135 g rotates about an axis perpendicular to the stick passing through the center of the stick with an angular speed of 3.50 rad/s squared. What is the magnitude of the angular momentum of the stick?

a. 0.0394 k x m squared/s.

b. 0.473 k x m squared/s.

c. 0.158 k x m squared/s.

d. 0.0236 k x m squared/s.

A figure skater is spinning slowly with arms outstretched. She brings her arms in close to her body and her moment of inertia decreases by 1/2. Her angular speed increases by a factor of:

a. 2.

b. 4.

c. The square root of (2).

d. 1/2.

A solid wood door, 90.0 cm wide by 2.00 m tall has a mass of 35.0 kg. It is ajar and at rest. A ball with a mass of 500 g is thrown perpendicular to the door with a speed of 20.0 m/s and hits the door 60.0 cm from the hinged side. The ball rebounds with a speed of 16.0 m/s along the same line. What is the angular speed of the door after the collision?

a. 0.127 rad/s

b. 0.925 rad/s

c. 1.14 rad/s

d. 4.57 rad/s

The torque required to turn the crank on an ice cream maker is 4.50 Nm. How much work does it take to turn the crank through 300 full turns?

a. 4240 J

b. 8480 J

c. 1350 J

d. 2700 J

An ice skater doing a spin pulls in her arms, decreasing her moment of inertia by a factor of two. How does her angular speed changes?

a. It is reduced by a factor of two.

b. It is reduced by a factor of four.

c. It increases by a factor of two.

d. It increases by a factor of four.

An astronaut is in a capsule in a stable orbit, about two Earth radii from the center of Earth. Her weight is:

a. Zero N.

b. The same as on the surface of Earth.

c. About one-half of her weight on the surface of Earth.

d. About one-quarter of her weight on the surface of Earth.

What would be the weight of a 59.1-kg astronaut on a planet twice as massive as Earth and having twice Earth's radius?

a. 580 N

b. 290 N

c. 1160 N

d. 118 N

What would be the weight of a 59.1-kg astronaut on a planet with the same density as Earth and having twice Earth's radius?

a. 580 N

b. 290 N

c. 1160 N

d. 2320 N

You are on an airplane traveling with a constant velocity at an altitude of 20,000 m. What is the acceleration of gravity at that altitude? The radius of Earth is 6.37 x 10 to power of (6) m.

a. 9.81 m/s squared

b. 9.78 m/s squared

c. 9.75 m/s squared

d. 9.72 m/s squared

The acceleration due to gravity on the surface of Earth is g. Calling R the radius of Earth, at what distance from Earth's center would the acceleration due to gravity drop to g/16?

a. 16 R

b. R/16

c. R/4

d. 4 R

Because Earth's orbit is slightly elliptical, Earth actually gets closer to the Sun during part of the year. When Earth is closer to the Sun its orbital speed is:

a. Less than when Earth is farthest away from the Sun

b. The same as when Earth is farthest away from the Sun.

c. Greater than when Earth is farthest away from the Sun.

d. Sometimes greater sometimes smaller than when Earth is farthest away from the Sun.

What is the ratio of potential energy to kinetic energy for a comet that has just enough energy to escape from the Sun's gravitational field?

a. 1/2

b. 1

c. 2

d. -1

The highest tides occur when:

a. The Sun and the Moon are on the same side of Earth.

b. The Sun and the Moon are on opposite sides of Earth.

c. The Sun, Moon, and Earth form a right-angled triangle with Earth at the 90 degree vertex.

d. The Sun, Moon, and Earth form a right-angled triangle with the Moon at the 90 degree vertex.

The quartz crystal in a digital watch has a frequency of 32.8 kHz. What is its period of oscillation?

a. 3.05 multiply 10 to power of (exponent) s

b. 9.58 multiply 10 to power of (exponent) s

c. 1.91 multiply 10 to power of (exponent) s

d. 9.71 multiply 10 to power of (exponent) s

If your heart is beating at 76.0 beats per minute, what is the frequency of your heart's oscillations?

a. 4560 Hz

b. 1450 Hz

c. 3.98 Hz

d. 1.27 Hz

The position of a mass that is oscillating on a spring is given by x = (18.3 cm) cos[(2.35 s to power of (-1))t]. What is the frequency of this motion?

a. 0.426 Hz

b. 1.34 Hz

c. 0.128 Hz

d. 0.374 Hz

In simple harmonic motion, the speed is greatest at that point in the cycle when:

a. The magnitude of the acceleration is a maximum.

b. The displacement is a maximum.

c. The magnitude of the acceleration is a minimum.

d. The potential energy is a maximum.

A sewing machine needle moves up and down in simple harmonic motion with an amplitude of 1.27 cm and a frequency of 2.55 Hz. What is the maximum speed of the needle?

a. 3.18 cm/s

b. 20.3 cm/s

c. 10.1 cm/s

d. 6.36 cm/s

How much work is required to stretch a spring 25.2 cm if its force constant is 12.3 N/m?

a. 0.391 J

b. 3.10 J

c. 1.05 J

d. 0.381 J

A harmonic wave has a wavelength of 2.0 m and a frequency of 5.0 Hz. What is the speed of the wave?

a. 10 m/s

b. 0.4 m/s

c. 0.10 m/s

d. 2.5 m/s

A harmonic wave travels with a speed of 200 m/s and has a wavelength of 0.800 m. What is the period of the wave?

a. 40.0 Hz

b. 125 Hz

c. 80.0 Hz

d. 250 Hz

A 6.00-m length of rope has a mass of 700 g. It is pulled taught with a force of 100 N. What is the speed of waves on the rope?

a. 29.3 m/s

b. 11.7 m/s

c. 42.0 m/s

d. 3.42 m/s

A 15.0-m rope is pulled taut with a tension of 140 N. It takes 0.545 s for a wave to propagate along the rope. What is the mass of the rope?

a. 1.67 kg

b. 2.77 kg

c. 5.09 kg

d. 3.19 kg

The vertical displacement of a string is given by y(x,t) = (6.00 mm) cos[(3.25 m to power of (-1)) x - (7.22 s to power of (-1))t]. What is the wavelength of the wave?

a. 1.93 m

b. 0.870 m

c. 0.308 m

d. 0.139 m

The pitch of a sound is determined by:

a. The amplitude.

b. The speed.

c. The frequency.

d. The wavelength.

Sound intensity is defined as:

a. The loudness of a sound.

b. The sound energy passing through a unit of area.

c. The sound power per unit volume.

d. The sound energy passing through a unit of area per unit time.

The density of air is 1.29 kg/m to power of (exponent). What is the mass of the air inside a room 4.0 m x 3.0 m x 2.0 m?

a. 3.1 kg

b. 31 kg

c. 1.9 kg

d. 19 kg

A 1938 nickel has a diameter of 21.21 mm, a thickness of 1.95 mm, and weighs 0.04905 N. What is its density?

a. 1.82 x 10 to power of (3) kg/m cubed.

b. 19.3 x 10 to power of (3) kg/m cubed.

c. 3.63 x 10 to power of (3) kg/m cubed.

d. 7.26 x 10 to power of (3) kg/m cubed.

A spar buoy consists of a circular cylinder, which floats with its axis oriented vertically. One such buoy has a radius of 1.00 m, a height of 2.00 m and weighs 40.0 kN. What portion of it is submerged when it is floating in fresh water?

a. 1.35 m

b. 1.30 m

c. 1.25 m

d. 1.20 m

An incompressible fluid flows steadily through a pipe that has a change in diameter. The fluid speed at a location where the pipe diameter is 8.0 cm is 1.28 m/s. What is the fluid speed at a location where the diameter has narrowed to 4.0 cm?

a. 0.32 m/s

b. 0.64 m/s

c. 2.56 m/s

d. 5.12 m/s