Standing Sound Waves- open tube

For this experiment the professor spun a tube and recorded the sound wave created by the tube. Using our knowledge of waves and their properties we calculated the length of the tube using the data recorded.

Light and Matter Waves

Diffraction

The purpose of this lab is to determine the distance (d) between grooves on a CD by diffraction.


We first arrange a laser so it shines on the disk and as it hits the grooves on the disk it causes diffraction. We measure the distance of the light difrracted from the middle to the point of first order maxima and the length from the light source to the wall where the light showing.

Since it causes constructive interference at the first maxima we used the formula

d*sin(theta) = m*lambda

and solve for d.

We see that the distance between grooves on a CD is about 1.5 micrometers.



Concave and Convex Mirrors

The pupose for this experiment is to observe the images formed by two different types of mirrors, concave and convex mirros. To analyze the characteristics of the images due to the curvature of the mirror, distance of the object to the mirror and reflected rays.





The first mirror we observed was a convex mirror.


We first placed an object in front of the mirror, the image appeared smaller than the actual object. The image was upright and was located inside the mirror, farther away relative to the distance of the mirror and object.

As the object is moved closer to the mirror, the image gets larger almost to its actual size.

As the object is moved away from the mirror the image gets smaller.



The second mirror was a concave mirror.

We first placed an object in front of the mirror the image appeared larger than the actual object and inverted, this is when the object was located behind the curvature point.

Once the object was moved closer the image was upright.

The image was located relatively closer than the mirror and object.















The magnification of the image is determined by using the lateral magnification:

m = y(i) / y(o) = -s(i) / s(o)

Where y(i) is the height of the image and y(o) is the height of the object.

s(i) is the distance from the mirror to the image and s(o) is the distance from the mirror to the object.



Standing Waves (short lab)

The purpose of this lab is to determine how frequency and wavelength are related.

First, we had two students hold each end of a spring. Then, we had the students create a standing wave by shaking the spring back and forth in the horizontal direction.

We first started with one wavelength and increased it by one for each trial, with a total of four trials. Two other students also time the amount it took for 20 waves and determined the frequency by dividing the total cycles by the amount of time.

This is the frequency that was determined:

Trial 1 : 2.35 Hz

Trial 2 : 2.86 Hz

Trial 3 : 1.67 Hz

After recording the data, it was then graphed and determined a relationship between wavelength and frequency. The wavelength and frequency seem to be inversely proportional to one another.



Standing Waves

The goal for this experiment is to investigate and have a basic understanding of force driven standing waves.

A standing wave is a transverse wave traveling along a medium, in this case a string, and then reflected back and returns interfering with other waves. When interfering, at resonance, a standing wave is created with nodes and antinodes in the wave pattern.

Equations:

-Transverse wave in the positive x direction.

y1 = A sin(kx - wt),

where k = 2*pi/lambda & w = 2*pi*f

-Transverse wave reflected from fixed end

y2 = A sin(kx + wt)

-At resonance, the two waves combine and become the some of both waves.

                                y = y1 + y2 = (2A sin (kx))*cos(wt)

 Other equations:

-Wavelength for each harmonic of vibrating string.

Lambda = 2L/n

-If frequency is known, the wave speed can be determined with fundamental wave velocity equation.

v = f*lambda

-Substituting both.

f = vn/2L

-velocity of wave traveling on a string.

v = sqrt(T/mu),

where T is tension & and mu is mass per unity length.

Experiment:

We used mechanism that drives a wave on one side of the string, and the other side of the string was pulled by a hanging mass creating tension. We adjusted the frequency of the driving mechanism to find each harmonic and measured the wavelength.

For case 1 we had a string of length 140 cm and a hanging mass of 200 g.

-Data:

16.5 Hz, 1 loop,  2 nodes, lambda 140 cm

32.5 Hz, 2 loops, 3 nodes, lambda 67 cm

45.6 Hz, 3 loops, 4 nodes, lambda 45 cm

56.7 Hz, 4 loops, 5 nodes, lambda 37 cm

74.6 Hz, 5 loops, 6 nodes, lambda 28 cm

87.4 Hz, 6 loops, 7 nodes, lambda 23 cm

For case 2 we had a string of length 186.5 cm and a hanging mass of 50 g.

Fluid Dynamics

In this experiment we filled a bucket with water and recorded the time elapsed as the water drained from a small hole at the bottom of the bucket. Then, calculated the theoretical time elapsed and compared both results.

Experiment: The bucket was filled with water 2.3 inches above the small hole, the hole had a diameter of approximately 0.6 centimeters. We ran six trials and recorded the time it took for 473 mL (16 ounces) of water to flow out of the bucket.




Volume emptied (V) = 16 ounces = 473 mL
 Height of water (h) = 2.3 in = 0.192 feet
 Area of drain hole (A) = pi*(.3cm)^2 = .28 cm^2 = 0.0003014 ft^2
 Acceleration due to gravity (g) = 32 ft/s^2

Trial #   time (t_actual)
1            25.06 s
2            24.85 s
3            25.24 s
4            25.36 s
5            25.17 s
6            26.09 s

The average of the six trials was 25.30 seconds. We then calculated the theoretical time by using the Flow rate equation, Continuity equation and Torricellis Theorem, which relates the speed of fluid flowing out an opening to the height of fluid above the opening.

R = V/t = Av  &  v = sqr(2gh)  ----->  V/t = A[sqr(2gh)]  ----> t(theoretical) = V/A[sqr(2gh)]    

                                                         

                                                         t (theoretical) = 15.14 s

Calculate Error:    |theoretical - actual|/theoretical x 100 = % error

                              |25.3s - 15.14s|/15.14 x 100 = 67% error

Comparing our measured value with the theoretical value gave us a 67% error. This does not agree within uncertainty. We then assumed that the measured diameter was inaccurate and decided to solve for the actual diameter using the same equations and the data recorded.

    

     v = sqr(2*32*0.192) = 3.505 ft/s,      R = V/t = (0.0160 ft^3)/25.30s = 6.324*10^-4 ft^3/s

                          V/t = A[sqr(2gh)] --- >  6.324*10^-4 ft^3/s = pi*r^2*3.505

                           r = 0.0076 ft = 0.28 cm, diameter = 0.56 cm

                          |0.6cm - 0.56cm|/0.6 x 100 = 6.67 % error

Here we see that our diameter should had been 0.56 cm. To check our result we compared both the calculated and measured diameters, this gave us a percent error of 6.67% which is within our uncertainty. This proves that our measurements were correct but there is still an unknown source that altered our results drastically.

There may be a few reasons why our result for our time had a big error. It is possible that we did not measured the height of the water correctly since we did not have a good angle reading the measurement while looking into the bucket. The increments on the beaker were not small enough to read exactly 473 mL, it was an approximate. Having better measuring equipment would had definitely lowered the error on our results.