Physics Oscillation and Wave Unit Vocabulary and Questions

Assume that wavelengths are propagating in a uniform medium. If the frequency of the wave source doubles then: A) The wavelength of the waves halves B) The wavelength of the waves doubles C) The speed of the waves halves D) The speed of the waves doubles

A) For a given medium, speed is constant. Doubling the frequency halves the wavelength

A vibrating tuning fork sends sound waves into the air surrounding it. During the time in which the tuning fork makes one complete vibration, the emitted wave travels: A) One wavelength B) About 340 meters C) A distance directly proportional to the square root of the air density D) A distance inversely proportional to the square root of the pressure

A) The time to make 1 cycle, is also the time it takes the wave to travel one wavelength

The figure above shows two wave pulses that are approaching each other. Which of the following best shows the shape of the resultant pulse when the centers of the pulses, points P and Q coincide? The figure has one wave, P, that is a square with an arrow to the right and the other is Q with an arrow to the left and a small box on top and another small box on the bottom. A) Large box to left B) One large one small box in middle C) One large box in middle D) One large box on top and another small box on bottom

A) Use superposition and overlap the waves to see the resultant

A small vibrating object on the surface of a ripple tank is the source of waves of frequency 20 Hz and speed 60 cm/s. If the source S is moving to the right, as shown, with speed 20 cm/s, at which of the labeled points will the frequency measured by a stationary observer be the greatest? A) A B) B C) C D) D

C) Clearly at point C the waves are compressed so are more frequent

A 0.1-kilogram block is attached to an initially unstretched spring of force constant k = 40 newtons per meter as shown above. The block is released from rest at time t=0. What will the resulting period of oscillation be? A) pi/40s B) pi/20s C) pi/10s D) pi/4s

C) Plug into period for mass-spring system T = 2(pi)sqrt(m/k)

Wavelength

The disturbance spanned by one cycle of motion; symbolized by upside down v, and because it is a length it is measured in meters

Sinusoidal

A graph or a funciton that has the form of a sine or cosine function; a continuous wave described in terms of sin and cos

Pendulum

A mass suspended from a pivot point by a light string or rod; oscillated about its equilibrium position; the force on a pendulum is a linear restoring force for small angles, so the pendulum does undergo simple harmonic motion

Physical Pendulum

A pendulum whose mass is distributed along its length; the position of the center of gravity of the physical pendulum is distance d from the pivot

Simple Harmonic Motion

A sinusoidal oscillation, often abbreviated SHM; a spherical type of oscillaiton motion where the restoring force is directly proportional to the displacement and acts in the direction opposite to the displacement

Medium

A substance that makes possible the transfer of energy from one location to another, especially through mechanical waves; as waves pass through a medium, the atoms that make up the medium are displaced from equilibrium

Small Angle Approximation

A useful simplification of the basic trigonometric functions which is approximately true in the limit where the angle approaches zero; restricting a pendulum's oscillations to small angles of 10º or less; measured in theta radians

Longitudinal Wave

A wave in which the particles in a medium move parallel to the direction in which the wave travels

Transverse Wave

A wave in which the particles in a medium move perpendicular to the direction in which the waves travel; a wave vibrating at right angles to the direction of its propagation

A 0.1-kilogram block is attached to an initially unstretched spring of force constant k = 40 newtons per meter as shown above. The block is released from rest at time t=0. What is the amplitude, in meters, of the resulting simple harmonic motion of the block? A) 1/40m B) 1/20m C) 1/4m D) 1/2m

A) At the current location all of the energy is gravitational potential. As the spring stretches to its max location all of that gravitational potential will become spring potential when it reaches its lowest point. When the box oscillates back up it will return to its original location converting all of its energy back to gravitational potential and will oscillate back and forth between these two positions. As such the maximum stretch bottom location represents twice the amplitude so simply halving the max ∆x will give the amplitude. Finding the max stretch: The initial height of the box h and the stretch ∆x have the same value (h=∆x)

A string is firmly attached to both ends. When a frequency of 60 Hz is applied, the string vibrates in the standing wave pattern shown. Assume the tension in the string and its mass per unit length do not change. Which of the following frequencies could NOT also produce a standing wave pattern in the string? A) 30 Hz B) 40 Hz C) 80 Hz D) 180 Hz

A) The given diagram is in the 3rd harmonic at 60 Hz. That means the fundamental is 20 Hz. The other possible standing waves should be multiples of 20

A particle oscillates up and down in simple harmonic motion. Its height y as a function of time t is shown in the diagram. At what time t does the particle achieve its maximum positive acceleration? A) 1 s B) 2 s C) 3 s D) 4 s

A) + Acceleration occurs when the mass is at negative displacements since the force will be acting in the opposite direction of the displacement to restore equilibrium Based on f=k∆x the most force, and therefore the most acceleration, occurs where the most displacement is

When an object oscillating in simple harmonic motion is at its maximum displacement from the equilibrium position. Which of the following is true of the values of its speed and the magnitude of the restoring force? SPEED RESTORING FORCE A) Zero Maximum B) Zero Zero C) Maximum 1/2 Maximum D) Maximum Zero

A) At T/4 the mass reaches maximum + displacement where the restoring force is at a maximum and pulling in the opposite direction and hence creating a negative acceleration. At maximum displacement the mass stops momentarily and has zero velocity.

A pendulum with a period of 1s on Earth, where the acceleration due to gravity is g, is taken to another planet where its period is 2s. The acceleration due to gravity on the other planet is most nearly: A) g/4 B) g/2 C) 2g D) 4g

A) Based on T = (2pi)sqrt(L/g), 1/4 g would double the period

The simple pendulum consists of a 1.0 kilogram brass bob on a string about 1.0 meters long. It has a period of 2.0 seconds. The pendulum would have a period of 1.0 seconds if the: A) String were replaced by one about 0.25 meter long B) String were replaced by one about 2.0 meters long C) Bob were replaced by a 0.25 kg brass sphere D) Bob were replaced by a 4.0 kg brass sphere

A) Based on T = (2pi)sqrt(L/g), 1/4 the length equates to 1/2 the period

The figure above shows a transverse wave traveling to the right at a particular instant of time. The period of the wave is 0.2s. Length of one wave is 5 cm. What is the amplitude of the wave? A) 4 cm B) 5 cm C) 8 cm D) 10 cm

A) By inspection

A mass m, attached to a horizontal massless spring with spring constant k, is set into simple harmonic motion. Its maximum displacement from its equilibrium position is A. What is the mass's speed as it passes through its equilibrium position? A) A•sqrt(k/m) B) A•sqrt(m/k) C) 1/A•sqrt(k/m) D) 1/A•sqrt(m/k)

A) Energy conservation: Usp = K 1/2KA^2 = 1/2mv^2

A sphere of mass m1, which is attached to a spring, is displaced downward from its equilibrium position as shown above left and released from rest. A sphere of mass m2, which is suspended from a string of length L, is displaced to the right as shown above right and released from rest so that it swings as a simple pendulum with small amplitude. Assume that both spheres undergo simple harmonic motion. Which of the following is true for both spheres? A) The maximum kinetic energy is attained as the sphere passes through its equilibrium position B) The maximum kinetic energy is attained as the sphere reaches its point of release C) The minimum gravitational potential energy is attained as the sphere passes through its equilibrium position D) The maximum gravitational potential energy attained when the sphere reaches the point of release E) The maximum total energy is attained only as the sphere passes through its equilibrium position

A) For the spring, equilibrium is shown where the maximum transfer of kinetic energy has occurred and likewise for the pendulum the bottom equilibrium position has the maximum transfer of potential energy into spring energy

If the frequency of the sound wave is doubled, the wavelength: A) Halves and the speed remains unchanged B) Doubles and the speed remains unchanged C) Halves and the speed halves D) Doubles and the speed doubles

A) Frequency and wavelength are inverses

A person vibrates the end of a string sending transverse waves down the string. If the person then doubles the rate at which he vibrates the string while maintaining the same tension, the speed of the waves: A) Is unchanged while the wavelength is halved B) Is unchanged while the wavelength is doubled C) Doubles while the wavelength is doubled D) Doubles while the wavelength is halved

A) Since the medium stays the same the speed remains constant. Based on v = f(upsidedown v) for constant speed, f and upside down v change as inverses

Multiple correct: A standing wave pattern is created on a guitar string as a person tunes the guitar by changing the tension in the string. Which of the following properties of the waves on the string will change as a result of adjusting only the tension in the string? Select two answers: A) The speed of the traveling wave that creates the pattern B) The wavelength of the standing wave C) The frequency of the standing wave D) The amplitude of the standing wave

A, C) Based on v = sqrt(F/(m/l)), the tension changes the speed. Then based on f = nv/2L, this resulting speed change will effect the frequency also. But since the frequency increases in direct proportion to the speed, and v = f(wavelength), the wavelength should remain unchanged. The equation of the wave speed is not required for this problem.

Multiple Correct: Two fire trucks have sirens that emit waves of the same frequency. As the fire trucks approach a person, the person hears a higher frequency from truck X than from truck Y. Which of the following statements about truck X can be correctly inferred from this information? Select two answers: A) It is traveling faster than truck Y B) It is closer to the person than truck Y C) It is speeding up, and truck Y is slowing down D) Its wavefronts are closer together than truck Y

A, D) Based on the Doppler effect, only speed matters. The faster a vehicle is moving, the closer together the sound waves get compressed and the higher the frequency. Take the case of a very fast vehicle traveling at the speed of sound; the compressions are all right on top of each other. So faster speed means closer compressions and higher frequencies. Choice I must be true because X is a higher frequency so must be going faster. Distance to the person affects the volume but not the pitch so the choice II is wrong. III seems correct but its not. It doesn't matter whether you are speeding up or slowing down, it only matters who is going faster. For example, suppose truck X was going 5 mph and speeding up while truck Y was going 50 mps and slowing down, this is an example of choice III but would not meet the requirement that X has a higher frequency because only actual speed matters, not what is happening to that speed.

Wave Model

Allows us to understand the many important features that different types of waves share; emphasizes the aspects of wave behavior common to all waves

Amplitude

An object's maximum displacement from its equilibrium with the object oscillating between x = -A and x = A; it is equal to one half the length of the vibration path

Traveling Wave

An organized disturbance that travels with a well-defined wave speed; a wave in which the medium moves in the direction of propagation

Damped Oscillations

An oscillation that runs down and stops; an oscillation in which the amplitude of the oscillating quantity decreases

Two wave pulses approach each other as seen in the figure. The wave pulses overlap at point P. Which diagram best represents that appearance of the wave pulses as they leave point P? There are two arrows in opposite directions, the boundary on the left has a square top and the boundary on the right has an upward down triangle. A) One arrow to the left, square, and triangle B) Two arrows both pointing outward with triangle on left square on right C) One arrow to the right, strange triangle on right D) One arrow to left, strange triangle on ledt

B) After waves interfere they move along as if they never met

A block on a horizontal frictionless plane is attached to a spring, as shown above. The block oscillates along with the x-axis with simple harmonic motion of amplitude A. Which of the following statements about the block is correct? A) At x = 0, its acceleration is at a maximum B) At x = A, its displacement is at a maximum C) At x = A, its velocity is at a maximum D) At x = A, its acceleration is zero

B) Basic fact about SHM, amplitude is max displacement

Assume the speed of sound is 340 m/s. One stereo loudspeaker produces a sound with a wavelength of 0.68 meters while the other speaker produces sound with a wavelength of 0.65 meters. What would be the resulting beat frequency? A) 3 Hz B) 23 Hz C) 511.5 Hz D) 11,333 Hz

B) Determine each separate frequency using the speed of sound as 340 and v = f(upsidedown v) then subtract the two frequencies to get the beat frequency

Referring to a graph below of the displacement x versus time for a particle in simple harmonic motion (The graph is a positive sine function): Which of the following graphs shows the kinetic energy K of the particle as a function of time t for one cycle of motion? A) Upward Quadratic B) Positive Cosine C) Translated Sine D) Sine Function

B) Energy will never be negative. The max kinetic occurs at zero displacement and the kinetic energy became zero when at the maximum displacement

The frequencies of the first two overtones (second and third harmonics) of a vibrating string are f and 3f/2. What is the fundamental frequency of this string? A) f/3 B) f/2 C) f D) 2f

B) Harmonics are multiples of the fundamental, so the fundamental must be f/2

An object swings on the end of a cord as a simple pendulum with period T. Another object oscillates up and down on the end of a vertical spring also with period T. If the masses of both objects are doubled, what are the new values for the periods? PENDULUM MASS ON SPRING A) T/sqrt(2) T•sqrt(2) B) T T•sqrt(2) C) T•sqrt(2) T D) T•sqrt(2) T/sqrt(2)

B) Pendulum is unaffected by mass. Mass-spring system has mass causing the T to change proportional to sqrt so since the mass is doubled the period is changing by sqrt(2)

Two wave pulses, each of wavelength v, are traveling toward each other along a rope as shown. When both pulses are in the region between points X and Y, which are a distance v apart, the shape of the rope is: A) Bump at right B) Straight C) Sinusoidal D) Bump at right downward

B) Superpose the two waves on top of each other to get the answer

A standing wave of frequency 5 Hz is set up on a string 2 meters long with notes at both ends and in the center, as shown above: The fundamental frequency of vibration of the string is: A) 1 Hz B) 2.5 Hz C) 5 Hz D) 10 Hz

B) The diagram shows the second harmonic in the string. Since harmonics are multiples, the first harmonic would be half of this

A small vibrating object S moves across the surface of a ripple tank producing the wave fronts shown above . The wave fronts move with speed v. The object is traveling in what direction and with what speed relative to the speed of the wave fronts produced? DIRECTION SPEED A) To the right Equal to v B) To the right Less than v C) To the left Less than v D) To the left Greater than v

B) The waves at the right are compressed because the object is moving right. However, the waves are moving faster than the object since they are out in front of where the object is

As sound travels from steel into air, both its speed and its: A) Wavelength increase B) Wavelength decrease C) Frequency increase D) Frequency remain unchanged

B) When sound travels into less dense medium, its speed decreases...however, like all waves when traveling between two mediums, the frequency remains constant. based on v = f(upsidedown v), if the speed decreases and the frequency is constant then the upsidedown v must decrease also

The graph below was produced by a microphone in front of a turning fork. It shows the voltage produced from the microphone as a function of time. The function is a cosine wave. In order to calculate the speed of sound from the graph, you would also need to know: A) Pitch B) Wavelength C) Frequency D) Volume

B) To use v = (f)(upsidedownv) you also need the upside down v

Multiple correct: In the doppler effect for sound waves, factors that affect the frequency that the observer hears include which of the following? Select two answers: A) The loudness of the sound B) The speed of the source C) The speed of the observer D) The phase angle

B, C) A fact about the doppler effect. Can also be seen from the doppler equation

Multiple correct. The diagrams above represent 5 different standing sound waves set up inside of a set of organ pipes 1 meter long. Which of the following statements correctly relates the frequencies of the organ pipes shown? Select two answers. A) Cy is twice the frequency of Cx B) Cz is five times the frequency of Cx C) Oy is twice the frequency of Ox D) Ox is twice the frequency of Cx

B,C) Wavelengths of each are (dist/cycle) ... 4L, 4/3L, 4/5L, L, 2/3L Frequencies are f = v/(upsidedownv) v/4L, 3v/4L, 5v/4L, 3v/2L --- Oy is 2x Cy

Two objects of equal mass hang from independent springs of unequal spring constant and oscillate up and down. The spring of greater spring constant must have the: A) Smaller amplitude of oscillation B) Larger amplitude of oscillation C) Shorter period of oscillation D) Longer period of oscillation

C) Based on T = (2pi)sqrt(m/k) the larger spring constant makes a smaller period

The figure above shows a transverse wave traveling to the right at a particular instant of time. The period of the wave is 0.2s. Length of one wave is 5 cm. What is the speed of the wave? A) 4 cm/s B) 25 cm/s C) 50 cm/s D) 100 cm/s

C) By inspection, the wavelength is 10 cm f = 1/T = 5 Then use v = wavelength(f)

Referring to a graph below of the displacement x versus time for a particle in simple harmonic motion (The graph is a positive sine function): Which of the following graphs shows the kinetic energy K of the particle as a function of its displacement x? A) Upward Quadratic B) Positive Linear C) Downward Quadratic D) Downward Sine Funciton

C) Energy will never be negative. The max kinetic occurs at zero displacement and the kinetic energy became zero when at the maximum displacement

If the speed of sound in air is 430 m/s, the length of the organ pipe, open at both ends, that can resonate at the fundamental frequency of 136 Hz, would be: A) 0.40 m B) 0.80 m C) 1.25 m D) 2.5 m

C) For an open-open pipe the harmonic frequency is given by f = nv/2L with n=1

What would be the wavelength of the fundamental and first two overtones produced by an organ pipe of length L that is closed at one end and open at the other? A) L, 1/2L, 1/4L B) 1/2L, 1/4L, 1/6L C) 4L, 4/3L, 4/5L D) 4L, 2L, L

C) Now the length of the tube remains constant and the wave is changing within the tube to make each successive waveform. Each upside down v is given by: upside down v = dist/cycle so: v1 = 4L v3 = 4/3 L v5 = 4/5L

The diagram shows two transverse pulses moving along a string. One pulse is moving to the right and the second is moving to the left. Both pulses reach point x at the same instant. What would be the resulting motion of point x as the two pulses pass each other? The arrow pointing to the left is in top of a triangle and the arrow pointing to the right is on top of an upside down triangle. The point x is directly in the middle of the two points. A) Down, up, down B) Up then down C) Up, down, up D) There would be no motion, the pulses cancel one another

C) Step the two pulses through each other a little bit at a time and use superposition to see how the amplitudes add. At first the amplitude jumps up rapidly, then the amplitude moves down as the rightmost negative pulse continues to propagate. At the very end of their passing the amplitude would be all the wave down and then once they pass the point will jump back up to the equilibrium

A block oscillates without friction on the end of a spring as shown. The minimum and maximum lengths of the spring as it oscillates are, respectively, Xmin and Xmax. The graphs can represent quantities associated with the oscillation as functions of the length x of the spring. Which graph can represent the kinetic energy of the block as a function of x? A) A B) B C) C D) D

C) The block momentarily stops at Xmin and Xmax, so must have zero K at these points. The box accelerates the most at the ends of the oscillation since the force is the greatest there. This changing acceleration means that the box gains speed quickly at first but not as quickly as it approaches equilibrium. This means that the KE gain starts off rapidly from the endpoints and gets less rapid as you approach equilibrium where there would be a maximum speed and maximum K, but zero force so less gain in speed. This results in the curved graph

A tube is open at both ends with the air oscillating in the 4th harmonic. How many displacement nodes are located within the tube? A) 2 B) 3 C) 4 D) 5

C) To produce pipe harmonics, the ends are always antinodes. The first (fundamental) harmonic is when there are tow antinodes on the end and one node in between. To move to each next harmonic, add another node in the middle and fill the necessary antinodes. (ex, 2nd harmonic is ANANA so the 4th harmonic is ANANANANA and have four notes

Multiple correct: One end of a horizontal string is fixed to a wall. A transverse wave pulse is generated at the other end, moves toward the wall as shown and is reflected at wall. Properties of the reflected pulse include which of the following? Select two answers: A) It has a greater speed than that of the incident pulse B) It has a greater amplitude than that of the incident pulse C) It is on the opposite side of the string from the incident pulse D) It has a smaller amplitude than that of the incident pulse

C, D) When hitting a fixed boundary, some of the wave is absorbed, some is reflected inverted. The reflected wave has less amplitude since some of the wave is absorbed, but since the string has not changed its properties the speed of the wave should remain unchanged

The standing wave pattern diagrammed to the right with a total length of 1.0 m is produced in a string fixed at both ends. The speed of waves in the string is 2 m/s. What is the frequency of the standing wave pattern? A) 0.25 Hz B) 1 Hz C) 2 Hz D) 4Hz

D) From diagram, wavelength = 0.5 m. Find the frequency with v = f(upsidedown v)

A simple pendulum and a mass hanging on a spring both have a period of 1s when set into small oscillatory motion on Earth. They are taken to Planet X, which has the same diameter as Earth but twice the mass. Which of the following statements is true about the periods of the two objects on Planet X compared to their periods on Earth? A) Both are shorter B) Both are the same C) The period of the mass on the spring is shorter; that of the pendulum is the same D) The period of the pendulum is shorter; that of the mass on the spring is the same

D) In a mass-spring system, both mass and spring constant (force constant) affect the period

The graph below was produced by a microphone in front of a turning fork. It shows the voltage produced from the microphone as a function of time. The function is a cosine wave. The frequency of the turning fork is approximately: A) 0.004s B) 0.020s C) 50 Hz D) 250 Hz

D) f = cycles/second

The graph shown represents the potential energy U as a function of displacement x for an object on the end of a spring moving back and forth with amplitude Xo. Which of the following graphs represents the kinetic energy K of the object as a function of displacement x? A) Upward Quadratic B) Upward Absolute Value Function C) Straight Line Above and Parallel to X-Axis D) Downward Quadratic

D) As the object oscillates, its total mechanical energy is conserved and transfers from U to K back and forth. The only graph that makes sense to have an equal switch throughout is D

An object is attached to a spring and oscillates with amplitude A and period T, as represented on the graph. The nature of the velocity v and acceleration a of the object at time T/4 is best represented by which of the following? A) v > 0, a > 0 B) v > 0, a < 0 C) v > 0, a = 0 D) v + 0, a < 0

D) At T/4 the mass reaches maximum + displacement where the restoring force is at a maximum and pulling in the opposite direction and hence creating a negative acceleration. At maximum displacement the mass stops momentarily and has zero velocity.

A ball is dropped from a height of 10 meters onto a hard surface so that the collision at the surface may be assumed elastic. Under such conditions the motion of the ball is: A) Simple harmonic with a period of about 1.4s B) Simple harmonic with a period of about 2.8s C) Simple harmonic with an amplitude of 5m D) Periodic with a period of about 2.8s but not simple harmonic

D) Based on free fall, the time to fall down would be 1.4 seconds. Since the collision with the ground is elastic, all of the energy will be returned to the ball and it will rise back up to its initial height completing 1 cycle in a total time of 2.8 seconds. It will continue doing this oscillating up and down. However, this is not simple harmonic because to be simple harmonic the force should vary directly proportional to the displacement but that is not the case in this situation

A standing wave of frequency 5 Hz is set up on a string 2 meters long with notes at both ends and in the center, as shown above: The speed at which waves propagate on the string is: A) 0.4 m/s B) 2.5 m/s C) 5 m/s D) 10 m/s

D) Based on the diagram, the wavelength is 2 meters Plug this into v = f(wavelength)

A block on a horizontal frictionless plane is attached to a spring, as shown above. The block oscillates along with the x-axis with simple harmonic motion of amplitude A. Which of the following statements about the energy is correct? A) he potential energy of the spring is at a maximum at x = 0 B) The potential energy of the spring is at a minimum at x = A C) The kinetic energy of the block is at a minimum at x = 0 D) The kinetic energy of the block is at a maximum at x = A

D) Basic fact about SHM, spring potential energy is a min at x=0 with no spring stretch

A mass m is attached to a spring with a spring constant K. If the mass is set into simple harmonic motion by a displacement d from its equilibrium position, what would be the speed, v, of the mass when it returns to the equilibrium position? A) v = sqrt(md/k) B) v = sqrt(kd/m) C) v = sqrt(kd/mg) D) v = d•sqrt(k/m)

D) Energy Conservation: Usp = K 1/2kd^2 = 1/2mv^2

Which of the following is true for a system consisting of a mass oscillating on the end of an ideal spring? A) The kinetic and potential energies are equal to each other at all times B) The kinetic and potential energies are both constant C) The maximum potential energy is achieved when the mass passes through its equilibrium position D) The maximum kinetic energy and maximum potential energy are equal, but occur at different times

D) Energy is conserved here and switches between kinetic and potential which have maximums at different locations

A mass m is attached to a vertical spring stretching it distance d. Then, the mass is set oscillating on a spring with an amplitude of A, the period of oscillation is proportional to: A) sqrt(d/g) B) sqrt(g/d) C) sqrt(d/mg) D) sqrt(m^2g/d)

D) First use the initial stretch to find the spring constant Fsp = mg = k∆x k = mg/d Plug into: T = 2(pi)sqrt(m/k)

A block oscillates without friction on the end of a spring as shown. The minimum and maximum lengths of the spring as it oscillates are, respectively, Xmin and Xmax. The graphs can represent quantities associated with the oscillation as functions of the length x of the spring. Which graph can represent the total mechanical energy of the block spring system as a function of x? A) A B) B C) C D) D

D) Only conservative forces are acting which means mechanical energy must be conserved so it stays constant as the mass oscillates

A pipe that is closed at one end and open at the other resonates at a fundamental frequency of 240 Hz. The next lowest/highest frequency it resonates at is most nearly: A) 80 Hz B) 120 Hz C) 480 Hz D) 720 Hz

D) Open-closed pipes only have odd multiples of harmonic so next f is 3x f1

A sphere of mass m1, which is attached to a spring, is displaced downward from its equilibrium position as shown above left and released from rest. A sphere of mass m2, which is suspended from a string of length L, is displaced to the right as shown above right and released from rest so that it swings as a simple pendulum with small amplitude. Assume that both spheres undergo simple harmonic motion. If both spheres have the same period of oscillation, which of the following is an expression for the spring constant: A) L/m1g B) g/m2L C) m2g/L D) m1g/L

D) Set period formulas equal to each other and rearrange for k

For a standing wave mode on a string fixed at both ends, adjacent antinodes are separated by a distance of 20 cm. Waves travel on this string at a speed of 1200 cm/s. At what frequency is the string vibrated to produce this standing wave? A) 120 Hz B) 60 Hz C) 40 Hz D) 30 Hz

D) Two antinodes by definition will be 1/2upside down v apart. So 20 cm = 1/2(upsidedown v) and the upsidedown v = 40 cm. Then using v = f(upsidedownv) we have: 1200 = f(40)

An ideal massless spring is fixed to the wall at one end, as shown above. A block of mass M attached to the other end of the spring oscillates with amplitude A on a frictionless, horizontal surface. The maximums peed of the block is Vm. The force constant of the spring is: A) mg/A B) MgVm/2A C) MVm^2/2A D)MVm^2/A^2

D) Using energy conservation: Usp = K 1/2kA^2 = 1/2mVm^2 Solve for k

A tube of length L1 is open at both ends. A second tube of length L2 is closed at one end and open at the other end. This second tube resonates at the same fundamental frequency as the first tube. What is the value of L2? A) 4L1 B) 2L1 C) L1 D) 1/2L1

D) We should look at the harmonic shapes open-open vs open-closed Comparing the fundamental harmonic of the open-open pipe to the closed-open pipe. The closed-open pipe should be half as long as the open-open pipe in order to fit the proper number of wavelengths of the same waveform to produce the given harmonic in each

Oscillation

Regular variation in magnitude or position around a central point; is a result of an interplay between the restoring force and an object's inertia, as the object moves through the equilibrium position repeatedly

Restoring Force

The force that brings an object back to its equilibrium position; if a system is brought away from its equilibrium position, the restoring force will tend to bring the system back toward equilibrium

Driving Frequency

The frequency of a system subjected to a periodic external force of frequency Fext; this frequency is completely independent of the oscillator's natural frequency F0

Natural Frequency

The frequency of an oscillating system that, when left to itself, oscillates at a frequency of F0; F0 is simply the frequency of the system if it is displaced from equilibrium and released

Frequency

The number of cycles per second, denoted by f = 1/T; the number of crests of a wave that move past a given point in a given unit of time; find by dividing the speed of the wave by the wavelength

Equilibrium Position

The position that an object rests at with no net force acting on it; the object has no further tendency to change at this position

Period

The time to complete one full cycle, given the symbol T; the time required for two successive wave crests to pass a fixed point

Hertz

The units of frequency, abbreviated by Hz; 1 Hz = 1 cycle per second = 1s^-1

Mechanical Waves

Waves that involve the movement of a substance through which they move, the medium; a wave that is an oscillation of matter, and therefore transfers energy through a medium

Driven Oscillation

When an oscillator is subjected to a periodic external force; applying a "driving force" to an oscillating system

Resonance

When the large amplitude response to a driving force whose frequency matches the natural frequency of a system; a vibrating system drives another system to oscillate with greater amplitude