# Standing Wave Lab Conclusion Essay

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• To determine the relation between the frequencies of resonant vibrations of a wire and the physical parameters of tension, length, and mass per unit length of the wire.

• To determine the relation between the velocity of waves on a wire and the tension and mass per unit length of the wire.

• Pasco Signal Generator

• 2 Banana leads 1.5 m long

• 2 alligator clips

• 2 meter ruler

• Large magnet

• 2 Table clamps

• Pulley, rods, weight set

• Resonance Wires with mass per unit length of about 0.02, 0.005, 0.002, 0.001, 0.0005, 0.0003 kg/m

• Graphical Analysis software

The relation between frequency, f, speed of wave propagation, v, and wavelength, λ, is given by

$$f = \frac{v}{\lambda}$$ (1)

The velocity of a wave in a string or wire will depend on the tension, T, and the mass per unit length (μ = m/L) of the string. When a string under tension is pulled sideways and released, the tension in the string is responsible for accelerating a particular segment back toward its equilibrium position. The acceleration and wave velocity increase with increasing tension in the string. Likewise, the wave velocity, v, is inversely related to the mass per unit length of the string. This is because it is more difficult to accelerate (and impart a large wave velocity) to a massive string compared to a light string. The exact relationship between the wave velocity, v, the tension, T, and the mass per length μ, is given by

$$v = \sqrt{\frac{T}{\mu}}$$ (2)

If a stretched string is clamped at both ends, traveling waves will reflect from the fixed ends, creating waves traveling in both directions. The incident and reflected waves will combine according to the superposition principle. As an example, when the string is vibrated at exactly the right frequency, a crest moving toward one end and a reflected trough will meet at some point along the string. The two waves will cancel at this point, this is called a node. The resulting pattern on the string is one in which the wave appears to stand still, and we have what is called a standing wave on the string. At the nodes, there is no motion in the string. The points which vibrate with maximum amplitude are called anti-nodes. If the string has length L and is fixed at both ends, the condition for achieving standing waves is that the length of the string be equal to a half-integral number of wavelengths.

$$L = n\frac{\lambda_n}{2} \mbox{ or } \frac{1}{\lambda_n} = \frac{n}{2L}$$ (3)

Combining eqs. (2) and (3) in eq. (1) gives,

$$f_n = \frac{v}{\lambda_n} = \frac{n}{2L} \sqrt{\frac{T}{\mu}}$$ (4)

as the basic model for a resonantly oscillating wire, where μ = m/L.

1. Secure the two table clamps on opposite ends of the table.

2. Attach the pulley in the table clamp away from the wall and clamp the short rod in the other.

3. Select a wire with a mass of about 0.005 kg/m that is about 1 m to 1.5 long with loops on each end.

4. Attach one loop of the wire to the short rod and hang the other end over the pulley.

5. Support about 500 g from the wire over the pulley end.

6. Connect the banana leads to the LO 8 Ω and GND terminals of the Pasco signal generator.

1. (red and black)

7. Connect the alligator clips to the other ends of the banana leads and to the ends of your resonance wire.

1. Make certain that the resonance wire is bare at the ends and any enamel is removed.

8. On the Signal Generator set the frequency range to the 1-100 position.

1. Make sure under Waveform the top, sine wave, is selected.

2. Turn the amplitude to in the mid-high range (see Figures 1 and 2).

1. Place the magnet in the center of the wire.

2. Beginning with a frequency of 0, gradually increase the frequency until the string vibrates resonantly, with one anti-node.

1. The string will be vibrating resonantly when it has the largest anti-node and a node that doesn’t move.

2. Record the frequency f, and the number n of anti-nodes: 1 in Table 1.

3. Move the magnet to where an anti-node will be next, and increase the frequency until you have two anti-nodes.

1. Record the frequency f, and the number n of anti-nodes: 2 in Table 1.

4. Repeat for number of anti-nodes, n, until you have 5 anti-nodes.

Graphical Analysis

1. Open Graphical Analysis.

2. Double click on the top of column X and rename n.

1. Enter in your values of the number of anti-nodes, n.

3. Double click on the top of column Y and rename fn.

1. Enter in your values of the frequency for each n.

4. Click on Analyze and Linear Fit to perform a linear fit of the data.

5. From eq. (4) you can see that the slope of your graph should be:$\left(\frac{1}{2L}\sqrt{\frac{T}{\mu}}\right)$ as $y = mx +b$ can be expressed as $f_n = \left(\frac{1}{2L}\sqrt{\frac{T}{\mu}}\right)n + 0$

1. Using the same wire from part 1, hang a 100 g weight from the wire.

2. Vary the frequency until you have resonance with n = 3. (3 anti-nodes)

3. Repeat with four more tension values between 1 N and 15 N (hanging masses between 100g and 1500g).

1. Use three anti-nodes, n = 3, in each step.

4. Record the values for mass, T = mg, and f3 in Table 2.

Graphical Analysis

1. Open Graphical Analysis.

2. Double click on the top of column X and rename T^(1/2).

1. Enter in your values of $\sqrt{T}$.

2. Note: You can easily use a new calculated column to calculate $\sqrt{T}$ from T.

3. Double click on the top of column Y and rename f3

1. Enter in your values for frequency.

4. Click on Analyze and Linear Fit to perform a linear fit of the data.

5. From eq. (4) the slope of the line should be. $$(\frac{3}{2L} \times \frac{1}{\sqrt{\mu}})$$ according to the equation $$f_3 = (\frac{3}{2L} \times \frac{1}{\sqrt{\mu}}) \sqrt{T}$$

1. Hang a 500 g mass from the wire.

2. Vary the frequency until there are 3 anti-nodes.

3. Record the frequency, f, mass per unit length of the wire, μ, and $\frac {1}{\sqrt{\mu}}$.

4. Repeat for 4 more wires of different mass per unit length, μ.

5. In Graphical Analysis, double click on the top of column X and rename 1/mu^(1/2).

1. Enter in your values of $\frac {1}{\sqrt{\mu}}$.

6. In the column for f3 enter in your values of the frequency.

7. Click on Analyze and Linear Fit to perform a linear fit of the data

8. From eq. (4), the slope of the line should be: $$(\frac{3 \sqrt{T}}{2L})$$ according to the equation $$f_3 = (\frac{3 \sqrt{T}}{2L}) \frac{1}{\sqrt{\mu}}$$

1. Design a lab to explore the relationship between length and frequency in a resonating wire.

2. Describe your experiment for determining the relationship between resonant frequency and length of wire.

3. Record the mass hanging from the wire.

4. Calculate the tension in the wire.

5. Record the fixed harmonic number for this experiment.

1. Describe your data collection techniques for showing that frequency is proportional to the harmonic number (n) (include a picture of your setup).

2. Record the length of the wire:

1. L =

3. Record the mass per unit length of the wire:

1. μ =

4. Record the mass hanging from the wire:

1. m =

5. Calculate the tension in the wire:

1. T = mg =

6. Record the resonant frequencies for each harmonic number in Table I below.

Table I: (title)

(you may need to select the table control in the upper left corner of the table, right click and select distribute rows evenly and distribute columns evenly then select borders and shading to turn on the grid)

Analysis

1. Insert a graph of frequency vs. harmonic number (n) including a linear fit.

2. Record the slope of the line:

1. slope =

3. Calculate the fundamental frequency using:

1. slope = $(\frac{1}{2L}\sqrt{\frac{T}{\mu}})$ =

4. Compute the difference between the fundamental frequency and the slope: $$\%Diff = \frac{|slope - f_1|}{f_1} \times 100\%$$

5. Record the value of the y-intercept:

1. b =

6. Qualitatively compare the %Diff with the estimated error from the y-intercept.

1. Explain why they are similar of different.

7. Calculate the wave velocity, v, two different ways:

1. First, use $v = \sqrt{\frac{T}{\mu}}$.

2. vfirst =

3. Second, $f_1 = \frac{1}{2L} \sqrt{\frac{T}{\mu}}$ use your fundamental frequency for f1 and solve for $\sqrt{\frac{T}{\mu}} = v$.

4. vsecond =

5. Compute the %Diff between these two calculations:$$\%Diff = \frac{|v_{first} - v_{second}}{v_{first}} \times 100\%$$

1. Describe your data collection techniques for showing that frequency is proportional to the square root of the tension (include a picture of your setup).

2. Record, n, the number of anti-nodes:

1. n = 3

3. Record the resonant frequencies for each hanging mass in Table II below.

Table II: (title)

m (kg) T = mg f3 (Hz)
0.10 1N
1.50 15N

(you may need to select the table control in the upper left corner of the table, right click and select distribute rows evenly and distribute columns evenly then select borders and shading to turn on the grid)

Analysis

1. Insert a graph of frequency vs. square-root of tension including a linear fit.

2. Calculate the expected value of the slope:

1. slopecalculated = $(\frac{3}{2L \sqrt \mu})$ =

3. Record the slope:

1. slopemeasured =

4. Compare the expected and actual slope: $$\%Diff = \frac{|slope_{calculated} - slope_{measured}|}{slope_{calculated}} \times 100\%$$ =

1. Describe your data collection techniques for showing that frequency is inversely proportional to the square-root of the mass/length of wire.

2. Record the mass hanging from the wire:

1. m =

3. Calculate the tension in the wire:

1. T = mg =

Record the fixed harmonic number for this experiment: n = 3.

Record the resonant frequencies for each wire weight in Table III below.

Table III: (title)

μ (kg/m)f3 (Hz)$$\frac {1}{\sqrt{\mu}}$$

(you may need to select the table control in the upper left corner of the table, right click and select distribute rows evenly and distribute columns evenly then select borders and shading to turn on the grid)

Analysis

1. Insert a graph of frequency vs. $$\frac {1}{\sqrt{\mu}}$$ including a linear fit.

2. Record the value of the slope:

1. slopemeasured =

3. Calculate the expected value of the slope:

1. slopecalculated = $\frac{3 \sqrt{T}}{2L}$ =

4. Compute %Diff between the expected and actual slope: $$\%Diff = \frac{|slope_{measured} - slope_{calc}|}{slope_{calc}} \times 100\%$$

## Further Investigation: /0

1. Describe your experiment for determining the relationship between resonant frequency and length of wire.

2. Record the mass hanging from the wire:

1. m =

3. Calculate the tension in the wire:

1. T = mg =

4. Record the fixed harmonic number for this experiment:

1. n = (three is probably easiest… but you can do whatever you want)

5. Record the resonant frequencies for each length in Table IV below.

Table IV: (title)

(you may need to select the table control in the upper left corner of the table, right click and select distribute rows evenly and distribute columns evenly then select borders and shading to turn on the grid)

1. Insert a graph of frequency vs. 1/L including a linear fit.

2. Record the slope of the line:

1. slopemeasured =

3. Calculate the expected value of the slope:

1. slopecalculated = $\frac{n}{2} \times \sqrt{\frac{T}{\mu}}$ =

4. Compare the expected and actual slope:

1. $$\%Diff = \frac{|slope_{measured} - slope_{calc}|}{slope_{calc}} \times 100\%$$

## Conclusion: /4

1. What is the relationship between the frequencies of resonant vibrations of a wire and the physical parameters of tension, length, and mass per unit length of the wire.

2. How did your lab support these relationships?

3. Did you get large %differences? If so, why?

4. What is the relationship between the velocity of waves on a wire and the tension and mass per unit length of the wire.

5. Did you like this lab?

6. Did you like labs?

7. What can we do to improve this lab, and lab in general?

8. etc…

## Abstract: /4

This is a formal statement of what this laboratory experiment was all about.

Included in this paragraph should be something about:

• The Objectives

## Certification: /2

• Include a statement that the work done in this lab and submitted in this report is yours and your partners.

EXAMPLE OF A WELL WRITTEN LAB REPORT FOR. Can time the speed of a slinky wave (exercise 1) and excite a standing half wave (one where. Question(s) in the Lab Report section. If the ends of a string or wire are fixed, standing waves can be set up. And the pin of the speaker using the two meter ruler; record this in your lab notebook. Standing (Transverse) Waves Using Vibrating Strings. How is a tsunami like a wave on a string? Physics 2310 Lab #1 Standing Waves on a String. What is the relationship between the tension in the string and the number of segments in the standing wave? Today, my classes completed the Cup Challenge, something you can get directions for from Science Gal. Experiment # 11: Mechanical Waves. Start studying PHYSICS LAB FINAL. String) can also travel through solids, and for these there are similar but slightly. Figure 1: The first three standing-wave modes of a string fixed at both ends and. THEORY: Standing waves can be produced when two waves of identical wavelength. Lab Procedure for Standing Waves on a String. Experiment as well as for the completion of the report. Physics Lab I. 16, Required: 1) a string vibration mount, 2) mass set, 3) lab stands, 4) slinky. This laboratory examines the principle on which most musical instruments operate and allows the student to observe standing waves, hear resonance and calculate the velocity of the waves. 10 Feb 2016 - 4 min - Uploaded by UNSW PhysicsThis is the lab video for the Standing Waves on a String experiment for Physics 1A. Duced by a vibrating guitar string, the sounds of a drum made by the vibrating drum head). This is called a “standing wave” for obvious reasons. What to Include in the Lab Report. Waves on a String, Wave Interference, Sound PhET Demonstration…12-23. The condition for achieving standing waves is that the length of the string. PHYSICS 1030L/1040L. Inman FW (2006) A Standing-Wave Experiment with a Guitar. Wavelength is twice the length of the vibrating section of the string, λ = 2L, where. A standing wave is a waveform where the nodes don't move. 0.4 Lab Report. A test concerning the principles of standing waves on a string was performed.

## Standing waves on a string lab report

(b) What tension in the string would be required to produce a standing wave with a wavelength equal to L1? This gives us a total of four antinodes; thus we are in the fourth harmonic. In this lab you will have the opportunity to explore various wave phenomena to help you organize your. Experiments can be done in the laboratory to determine wavelength of visible light. Contact · Privacy policy · Report a bug. The string-bending model is experimentally validated using a variety of strings. Studying the standing waves in a stretched string of a fixed length L under a variable tension. The goal of this. The vibrator used in this laboratory is driven by an electromagnet at a fre- quency of 60 Hz, but. String and standing waves, speed of sound apparatus, Young's Modulus apparatus, simple pendulum and. However, in this experiment the string vibrator has only one frequency. STANDING WAVES. Download the Standing Waves on Coil Springs Lab. (b) If you have. What to learn and explore. HIS MANUAL COVERS the physics of waves, sound, music, and musical instruments at a level. PHYSICS 126 Laboratory Manual. The physics and musical applications of strings are discussed in Strings, standing waves and harmonics. Your teacher will perform the. [SSM] Two rectangular wave pulses are traveling in opposite directions along a string. 8 Standing Waves on a String. A detailed description of the requirements for the lab report is given in the “Lab Report. S3P-1-02 Describe. This photo illustrates a standing wave created by quickly spinning a string of Christmas lights.
Physics Laboratory I, earlier known as Measurement Techniques I. The report during the lab period. Waves (actually forming standing, resonant waves) on the string and its length. In this lab, you will measure the first 6 resonance frequencies f1, f2, …, f6, and find. Some questions based on Melde's vibrating string experiment. Standing Waves on a Vibrating String. Grade (equivalent to one formal lab report) on the quality of your lab notes. PHET string wave demos of reflection and interference. Lab report on blood pressure · standing waves on a string lab report. Research and write an introduction to your lab report sharing what you. They are tones caused by standing waves produced in or on the instrument. This section includes an outline for your lab reports and a sample lab report based. Standing Waves in a String Laboratory Report.
In class lab report for that experiment will be due at the end of the class.