DescriptionStanding Waves on a String (Online)

Objective:

The purpose of this experiment is to generate a transverse wave on a string and measure the tension that causes a

standing wave. Using the tension to observe the relationship between tension and the wavelength. Finally to confirm

the wave relationship = holds.

Equipment:

•

•

Online Simulation https://ophysics.com/w8.html

Excel, Google Sheets, or other spreadsheet program.

Overview:

With a stretched string, the wave the travels along the string is defined by the tension and linear mass density. The

equation can be written as

string = √

If one end of the string is held fixed and the other end is attached to a vibrator that oscillates in the vertical direction.

These waves will be reflected off the fixed end and will be inverted such that the two waves will then interfere. If the

tension is adjusted just right a standing wave will be produced. The figure below shows the following wave patterns with

increasing numbers of “loops.” These are points where the string has maximum displacements.

Procedure:

1. Open the simulation. Set the frequency to as close to 120 Hz as possible. Record your frequency value in Table 1

in the actual column. Set the linear mass density to something around 0.42 × 10−3 kg/m. Record the length

between the oscillator and the pulley. Calculate the wavelength, , for each number of loops and record in Table

1.

2. Using the Tension slider change the tension in the string until you get 5 loops.

3. In Table 1 record the tension. Use the equation for the speed of the wave on a string = √ to solve for the

velocity of the wave. Finally use the fundamental wave property = to solve for the frequency. Record in

Table 1.

4. Using the frequency in step 3 compare that to the actual frequency set by the simulation. Use the percent error

calculation. Record your value in Table 1.

5. Repeat this step for “loops” 4, 3, and 2.

Table 1

Number of

“loops” (n)

= (m)

Tension (N)

= √ (m/s)

= (Hz)

actual (Hz)

Percent error

5

4

3

2

6. Using a spreadsheet program plot the square root of the tension as a function of the wavelength. This means

your y-axis should be the √ and your x-axis should be .

7. Add a trendline to your graph. Add your graph with the trendline in the space below.

8. The slope of the trendline should be equal to the product of the frequency and the square root of the linear

density. Record the slope below and your calculation for √ . Record your observations on if the two are close

below.

9. Make a prediction on the tension force required to get a single loop (n=1). Show all your work below. You can

insert a picture of your work.

10. Since the force is too large for the simulation, suggest a way to modify your setup in the simulation to allow a

single loop standing wave. Record your suggestion below.

11. Using the new modified setup calculate the theoretical tension required. Record your calculations below. Linear

12. In the simulation adjust the parameter you suggested in step 9 and find the tension required for a single loop.

Record this actual tension.

13. Calculate the percent error between the tension you found in step 11 and that you found in step 12. Record

your answer below.

The Simple Pendulum

Dr. Jonathan Meair

A simple pendulum takes the same amount of time to complete

each cycle of its motion. When considering what could affect

the time per cycle or period of the motion, we can consider at

least three factors:

•

•

•

The amplitude of the swing

The mass of the pendulum bob

The length of the pendulum

To determine how these factors affect the pendulum period,

you can do a controlled experiment in which the period of

oscillation is measured while only changing one variable at a

time. In this experiment, you will use a stopwatch to measure

the period of a pendulum and determine how it is affected by

each of the described factors.

Learning Objectives

1.

Students will determine how the period of a simple

pendulum depends on its amplitude, mass, and length.

Materials

You will need string and some objects to hang from it. For string you can use dental floss, thread

from a sewing kit, fishing line, shoe laces, etc. Be creative, but be sure that the mass you hang

from it is much heavier than the string.

To make measurements you will need a stopwatch (such as the one on your cell phone) and a

ruler or some other precise measurement tool. If you cannot find a ruler, remember that US letter

paper is 8.5 X 11.0 inches and 1 inch = 2.54 cm. You should be able to do a fine job making

length measurements if you put in the effort.

1 of 6

Name: ___________________________________________________________

Date: _____________________

Experiment 1

1.

Cut a string that is at least 1 meter long and tie it to something stable so that it hangs

vertically. Hang an object from the free end of the string. Time how long it takes for 10

cycles to occur. Record the value:

t = _________

2.

What is the period of the oscillation? Show your work.

T = _____________

3.

Repeat the experiment several times, but releasing the mass at different initial angles (but

smaller than 30 degrees.) Record the periods below.

T1 = ____________

4.

T2 = _____________

T3 = ____________ T4 = ____________

Did the angular amplitude of the oscillation have a significant effect on the period of

oscillation? Is this consistent with the theoretical model for the period of oscillation of a

pendulum? Carefully explain your answer using well-written complete sentences.

2 of 6

Name: ___________________________________________________________

Date: _____________________

Experiment 2

5.

Repeat experiment 1, except this time use a consistent angular amplitude but change the

object that you hang with objects of different weights. Be careful to make sure that the

length of the pendulum as measured from the point of support to the center of mass of the

hanging object does not change from one trial to the next. Record the period for each of

the trials below.

T1 = ____________

6.

T2 = _____________

T3 = ____________ T4 = ____________

Did the mass of the hanging object have a significant effect on the period of oscillation?

Is this consistent with the theoretical model for the period of oscillation of a pendulum?

Carefully explain your answer using well-written complete sentences.

3 of 6

Name: ___________________________________________________________

Date: _____________________

Experiment 3

7.

Choose one mass and one angular

amplitude to work with. Record the

period of oscillation (based on 10

complete oscillations) for 6 different

pendulum lengths between 0.25

meters and 2 meters. Create a table

with two columns in which to record

your data. The first column should

be the pendulum length L and the

second should be the period T.

Record your data.

8.

Carefully create a scatter plot of the period squared (T2) versus the pendulum length (L).

Carefully label axes and add a trend-line. Be sure to display the equation on the chart. See

the instructional video on graphing with Microsoft Excel. Also see the “Data Analysis

and Graphing” instruction file for information about graph formatting. Include a

screenshot of your graph here or attach a scanned copy of your graph to the back of this

document.

4 of 6

Name: ___________________________________________________________

Date: _____________________

9. Use the model for how the period of a pendulum squared depends on its length along

with the fit parameters of your linear fit to determine an experimental value for the freefall gravitation acceleration on Earth. You may not need both fit parameters. Show your

work. (You may find it helpful to review the “Data Analysis and Graphing” instruction

file to assist in understanding how to compare models to fit equations.)

10. What is the percent error in your experimental value for the free-fall gravitational

acceleration (g) of Earth? Show your work.

5 of 6

Name: ___________________________________________________________

Date: _____________________

11. Conclusion Question: According to the model, how does the period of a pendulum

swing depend on its length? Carefully state the mathematical relationship between them.

Does your experiment confirm this relationship? Justify your answer by referencing

important features in your graph. Carefully explain your answer using well-written

complete sentences.

12. Take a picture of your experimental setup (including the objects used) and put it in the

space below.

6 of 6

Purchase answer to see full

attachment

#### Why Choose Us

- 100% non-plagiarized Papers
- 24/7 /365 Service Available
- Affordable Prices
- Any Paper, Urgency, and Subject
- Will complete your papers in 6 hours
- On-time Delivery
- Money-back and Privacy guarantees
- Unlimited Amendments upon request
- Satisfaction guarantee

#### How it Works

- Click on the “Place Your Order” tab at the top menu or “Order Now” icon at the bottom and a new page will appear with an order form to be filled.
- Fill in your paper’s requirements in the "
**PAPER DETAILS**" section. - Fill in your paper’s academic level, deadline, and the required number of pages from the drop-down menus.
- Click “
**CREATE ACCOUNT & SIGN IN**” to enter your registration details and get an account with us for record-keeping and then, click on “PROCEED TO CHECKOUT” at the bottom of the page. - From there, the payment sections will show, follow the guided payment process and your order will be available for our writing team to work on it.