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Diffraction Patterns and Torque

APQ diffraction pattern (09)

Directions: Solve the following problems.  Each is worth 3 points

 

1)      Light of wavelength 650 nm strikes two slits and creates a diffraction gating on a screen that is 3 m away.  If the maxima are separated by 2 cm, determine the separation of the slits.


2)      Light of wavelength of 650 nm strikes a single slit.  This creates a central maxima that is 2 cm wide on a screen that is 3 m away.  Determine the width of the slit.

3)      Determine the location of the 1st maxima on a screen 3 m away if light of 550 nm strikes a diffraction grating having 2,000 lines per mm.

 

Doppler & Shock Waves



1)      A siren will wail at 106 db and 1250 Hz.  If the siren is stationary, and you move toward it at 22 m/s, what pitch sound will you hear?

 

2)      The same siren  as in #3, only this siren is mounted on a police car, which is moving toward you at 25 m/s.

3)      While riding in a boat, you approximate the angle of the wave produced by the boat to be 30 degrees from the direction of travel of the boat.  You notice the boat is traveling at 12 m/s, so what is the speed of the waves in the water?

4)      When working with multiple objects moving and the Doppler effect, does it work to simply use relative motion?  Defend your answer

 

 

 

Gauss’ Law

 

1)      A donut ( a real donut…think glazed Maple Donut….) has a hole in the center of radius “r”.  The donut as a whole has a radius of R.  There is a charge distribution of q/m3 in the dough of the donut.  (Ok, let’s simplify this a little…think of the donut more as a slice of a “hollowed” cylinder….the irregular roundness of the real donuts sends this problem beyond the scope of this course)

a.       Determine an expression to determine the electric field at any location inside the whole of the donut. (less than r)

b.      Determine an expression to determine the electric field at any location within the “dough” of the donut. (greater than r, less than R)

c.       Determine an expression to determine the electric field at any location beyond the dough of the donut. ) Positions greater than R.

2)      In Gauss’s Law for Electric Field, , what represents the surface area of the Gaussian surface?

3)      Determine the dipole moment on a particle if the if a 0.06 N/C field produces a torque of 3x10-3Nm

 

4)      Determine the electric flux if our area is this paper (8.5 inches x 11inches) and the electric field is directed from the bottom of this paper toward the top with a magnitude of 2 N/C.

 

Intro To Waves

 

1) While riding an upward moving open elevator, you drop (initial velocity relative to you is zero) a stone over the edge of the elevator floor.  Determine how high you were when you dropped the stone if it took 8.3 seconds for the stone to hit the ground while the elevator was moving upward at 6 m/s.

2)      Describe the following terms.  Use diagrams and pictures whenever appropriate:  Amplitude, frequency, wavelength, longitudinal, transverse

3)      3) While sitting on a dock by the bay, you notice that a wave smacks a piling of the dock once every .75 seconds.  You approximate the wavelength to be about 22 cm.  Knowing that the speed of a wave in any medium is constant, determine the wavelength of waves that strike the piling once every 1.8 seconds.


4) A sound wave has an intensity of 25 J/m2s 1.25 m away from a speaker.  Determine the intensity 5 m away from the speaker.  (Think about how this relates to using headphone, or in-ear phones, in relation to listening to speakers placed on the far side of the room.)

5) Determine the wavelength of a sound wave that has a frequency of 1,200 Hz.  (Sound travels through air at approx 330m/s).




6) A wave on a string is such that there is a single, fundamental frequency on a 0.75 m of cord.  Determine the wavelength of the wave.

 

7) Determine the fundamental frequency of vibrating string that is 2.3m long, has a mass of 0.005kg, and has a tension of  340N.



8) Using a diagram, demonstrate constructive and destructive interference in waves.

 

Rayleigh & Polarization

 

1)      Determine the intensity of light that is able to pas through 4 polarization filters.  The second filter is oriented at 12 degrees to the first, the 3rd is oriented at 22 degrees to the 2nd, and the 4th is oriented at 39 degrees to the 3rd.

2)      A thin film of index of refraction of 1.4 has incident light of 550 nm.  Determine the thickness of the material such that no reflected light is visible.

3)      A thin film of index of refraction of 1.4is layered on top of another film of index 1.6, and this all has incident light of 550 nm.  Determine the thickness of the material such that no reflected light is visible.

4)      Headlights from a car are 1 m apart.  If we assume that the light is of wavelength 450nm and your eye opening is 3mm in diameter.  What is the greatest distance the car can be away and still be resolved as two headlights?  (At this distance, you can’t tell if it is a motorcycle or a car.)

 

SHM

 

1)      A 135kg cart is sprung with a 550N/m spring.  Determine the frequency of oscillation when the cart hits a bump.

2)      A block of 25 kg is supported by two springs, each with a spring constant of 25 N/m. The two springs are side-by side, not one connected to the other. Determine the period of oscillation if the block is set into motion.

3)      Determine the natural frequency of vibration for a 0.36 kg mass that is attached to a 178N/m spring.

4)      A pendulum oscillates 32 oscillations in a time of 12 seconds. Determine the length of the pendulum.

5)      A 0.5 kg mass attached to a 12 N/m spring is held 4 m from the equilibrium point.  The mass is released at t=0.  Determine the position of the mass 3 seconds after it is released. (Keep in mind the nature of the motion.  You should be able to reason your way through an equation that will allow you to determine the position.

6)      Using a diagram, indicate how the acceleration, velocity, and position of an object in simple harmonic motion are represented in part by circular motion.

Sound Intensity

 

1)      A child on a merry-go-round is moving with a speed of 2.4 m/s when 1.2 m from the center of the merry-go-round.  Determine the centripetal acceleration of the child.

 

2)      A string will break if more than 60 N are applied to the string.  This 0.6m long string is attached to a 0.4kg ball and spun around.  Determine the speed that the ball goes flying off with when the string breaks.

 

3)      Calculate the acceleration due to gravity on the surface of the moon knowing that the moon has a mass of 7.35x1022kg and a radius of 1.74x106m.

 

4)      What is the difference between diffraction and refraction?

 

5)      What is the intensity level (db) for a sound that’s intensity is 2.0x10-6W/m2?

 

6)      A 76 db sound strikes an eardrum with a surface area of 5.0x10-5m2.  Determine how much energy strikes the eardrum per second.

7)      At a rock band concert, a dB meter read 130dB when placed 1.4 m in front of a speaker.  Determine the power output of the speaker.  Assume the wave radiates in a perfect sphere, and no energy is lost to the air.

 

First Test First Marking Period

AP 1st test 1stmk (09)

 

 

1.      Using a sketch, show free end  reflection of a wave.

2.      A string of length 1.5 m vibrates at the 1st harmonic of 20 Hz.  Determine the 2nd harmonic, the 1st overtone, and  the 3rd harmonic.

3.      Using a sketch, show constructive and destructive interference.

4.      Sketch two waves that are in phase with each other.

5.      A water wave approaches a shoal resulting in the wave speed changing from 2.8m/s to 2.1 m/s.  If the incident wave strikes at a 34 degree angle with the normal, determine the angle of refraction.

6.      A string of length 12 meters has a mass of 0.5 kg.  A pulse is sent the length of the string which is being held with a tension of 14 N.  Determine how long it will take the pulse to return to you.

7.      Determine the wavelength of a 300 Hz sound, realizing that the speed of sound is approximately 330 m/s.

8.      Consider  the discussion in the text regarding the relationship between wave energy and wave intensity.  How do these two terms differ?

9.      Your textbook engaged in a discussion of 3 dimensional waves and the relationship of amplitude to distance traveled of the wave.  What is the relationship between the amplitude and distance traveled for a 1 dimensional wave?

 

10. Define refraction

 

11. Define of diffraction.

 

Test #2 first marking period

 

 

1.      An object is 3 m in of a convex mirror.  The mirror has a radius of curvature of 20cm.  Determine the location of the image.

2.      Light of wavelength 550nm barely kicks out an electron from the surface.  Determine the work function of the material.

 

3.      Light of wavelength 550 nm is scattered by 20 degrees from it’s incident direction.  Determine the wavelength of the scattered light.

 

4.      An open pipe is attached to the top of your car.  While driving down the road, it begins to whistle.  If both ends of the pipe are open, and the pipe is 2.2 m long, determine the frequency of sound “created” by driving down the road.  You are driving at 22 m/s

 

5.      While driving at 20 m/s you blow your horn (car horn that is…) which is designed to make a sound at 2,000 Hz.  Determine the frequency heard by a car coming at you that is also traveling at 20m/s.

 

6.      A boat is traveling through the water at 60mi/hr.  The waves created by the boat make an angle of 25 degrees from a line bisecting the boat.  Determine the speed of the water waves.

 

  1. At a movie theatre, a sound pressure meter read 110dB when placed 0.4 m in front of a speaker.  Determine the power output of the speaker.  Assume the wave radiates in a perfect sphere, and no energy is lost to the air.

 

 

Test #3

1)      Light is incident on a cube of clear “plastic” that has a index of refraction of 1.8.  The incident angle on the cube is 58 degrees.  Determine the refracted angle of the light leaving the cube.

 

2)      Determine the critical angle for total internal reflection for light incident on an interior surface of a material with an index of refraction of 2.1.

 

3)      You are standing 3 m directly in front of a flat mirror.  You see yourself.  Determine how far (in degrees) you would need to rotate the mirror to view someone that is standing 3 m to your left side.

 

4)      Using a scale ray tracing, locate the image for a 2 cm tall object that is 5 cm from a lens of diopter 50.

 

5)      Using a scale ray tracing, locate the image for a 2 cm tall object that is 5 cm from a lens of diopter -50.

 

6)      Using the lens equation, determine the location of an image using a lens of diopter  10 when the object is 2 m away.