Physics assignments (urgent !!)

PHYS 150 NAME:

Homework Assignment: Standing Waves on a String Refer to Chapter 11 in your text

Due Date: Tuesday, June 18, 2016, at the beginning of class

You may print this sheet and write your answers on it, or write your answers on separate pages (be sure to clearly label each question

& answer.)

Open a web browser, and navigate to the following web page:

http://serc.carleton.edu/student_videos/index.html#waves

Look for the video called “Standing Waves.” Click the DMV player link and start the video. You should see a

frame like Figure 1 below:

Figure 1: Screenshot using DMV player

Using the video controls, you can advance the video one frame at a time. The red LED display on screen

indicates the frequency of the motor used to oscillate the string (you can see the motor attached to the right end

of the string). The tension in the string is caused by the 50-gram mass hanging from the left end.

As the video plays, the motor frequency is steadily increased. You will see several harmonic modes appear

(standing waves consisting of loops on the string). Play the entire video completely before you begin, then reset

before you answer the following questions.

1. If there is a 50-gram mass hanging in equilibrium on one end of the string, calculate the tension in the string

in Newtons:

2. Click the Horizontal Ruler button, and carefully position the ruler (click and drag) until the 0 cm mark lines

up with the left edge of the horizontal portion of string, as shown below in Fig. 2.

3. What is the length of the string (to the nearest cm)? Measure to the center of the vertical shaft of the motor

on the right side.

L = _________________________

4. Play the video, and pause the video when you see the first harmonic mode appear (one loop). Use the single-

frame forward and reverse buttons to make sure that you find the frame with the highest-amplitude loop. What

is the frequency corresponding to this loop (the fundamental frequency of the string):

f1 = ___________________________

5. What is the wavelength corresponding to the fundamental frequency?

1 = ___________________________

6. What is the speed of the waves on the string? (Use wavelength and frequency to calculate.)

v1 = __________________________

7. If the tension in the string remains the same, and if the string’s mass density remains the same, what will be

the speed of the waves when you see the second harmonic mode appear (two loops)?

v2 = __________________________

8. If the string is divided into two loops, what will be the wavelength corresponding to the second harmonic

mode?

2 = ___________________________

9. Calculate the second harmonic frequency using speed and wavelength:

f2 = ___________________________ (Calculated)

10. Now play the video until you see two loops appear. Pause the video, and use the single-frame forward and

reverse buttons until you find the frame with the highest-amplitude loops. Record the frequency displayed on

screen:

f2 = ___________________________ (On Screen)

11. The on-screen frequency should be close to your calculated frequency. How close? Calculate the percent

difference between the two numbers (the difference divided by average . . . refer to previous assignments for

examples): * Do not turn in this assignment until your percent difference is less than 10% . . .

If it is greater than 10%, you need to check your calculations, or perhaps your on-screen data.

12. Now calculate the third and fourth harmonic frequencies, along with the corresponding wavelengths:

Third Harmonic: f3 = _________  = _____________

Fourth Harmonic: f4 = _________  = _____________

13. Do you third and fourth harmonic frequencies match the on-screen frequencies, within a 10% difference?

(They should.) Show your percent difference calculations.

14. Use your calculated speed of the waves on the screen, and the tension in the string, to calculate the linear

mass density () of the string (in kilograms per meter):

15. If you double the tension in the string, but keep the mass density and length the same, what will be the new

fundamental frequency? (Show all of your steps below.)

New f1 = ___________________________ (Calculated)

16. On the video, use the pull-down menu at the bottom of the screen to select the 100-gram mass on the end of

the string. Play the video, and determine the new fundamental frequency for the string:

New f1 = ___________________________ (On Screen)

17. Calculate the percent difference between the on-screen and calculated values for new f1. Is the percent

difference less than 10%?

18. If the percent difference is higher than expected, first check your calculations, then your on-screen

observations. If those seem OK, then the reason for the difference may be a change in the string’s linear mass

density. (In other words, by adding tension to the elastic string, we inadvertently changed , as well.)

The string is elastic, which means that it will stretch when more tension is applied. If the string stretches, its

linear mass density will change.

If the string stretches, will its linear mass density increase or decrease? Explain your answer.