string vibration experiment

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Vibrating string lab report with graphs and question

General physics laboratory i (phys 201l), university of south carolina, recommended for you, students also viewed.

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Eric Son, Michael Campbell Department of Physics and Astronomy, University of South Carolina PHYS 201L: General Physics I Lab Ms. Alexis Osmond Nov 29, 2021 Abstract

The main objective of this experiment was to observe and verify the relationship between frequency, tension, wavelength, and speed. We were able to conduct the experiment by using a PASCO vibrator. We have attached a string on both the vibrator and the weight holder and placed the weight holder over the pully, hanging it in the air. Placing a certain weight on the weight holder increased the tension on the string causing it to make certain number of loops. Our goal was to successfully make 1, 2, 3, 4, and 5 stable loops throughout the experiment. By hanging 420g for 1 loop, 100g for 2 loops, 42g for 3 loops, 20g for 4 loops and 10g for 5 loops,

results for the loop length for each number of loops were: 1m for 1 loop, 0 for 2 loops, 0 for 3 loops, 0 for 4 loops and 0 for 5 loops.

Introduction

The purpose of vibrating string lab is to find the frequency at different weights. In this experiment, there will be a string, a pulley system and a device used to vibrate the string. With every bit of weight added the string will make loops at certain numbers of mass. The main goal of this lab is to verify the relationship between frequency, tension, speed, and wavelength.

Formulas used in this experiment are: m*g for tension, √𝑇𝜌 for wave propagation speed, and 𝑉𝜆 for

the frequency.

See project outline for procedure.

Hanging Mass (g)

Tension (mN)

Wave propagation speed (m/s)

Frequency (Hz)

1 1 m 420 g 4120 mN 111 m/s 55 Hz 2 0 m 100 g 981 mN 54 m/s 54 Hz 3 0 m 42 g 412 mN 35 m/s 53 Hz 4 0 m 20 g 196 mN 24 m/s 48 Hz 5 0 m 10 g 98 mN 17 m/s 43 Hz Table 1. Lab results for the vibrating string experiment

loops: 981 mN, for 3 loops: 412 mN, for 4 loops 196 mN, and the finally for 5 loops, 98.

mN. Wavelength propagation was calculated by using the following formula: √𝑇𝜌. With 𝜌 being

the linear mass density we’ve calculated at the very beginning, the wavelength propagation speed for each trial came out to be 117 m/s for 1 loop, 54 m/s for 2 loops, 35 m/s for 3 loops, 24. m/s for 4 loops, and 17 m/s for 5 loops. Lastly frequency was calculated by using the following

formula: 𝑉𝜆. 𝑉 represents the wavelength propagating speed, and 𝜆 represents the wavelength,

which is calculated by simply multiplying 2 to each loop length. The frequency for 1 loop came out to be 55 Hz, 54 Hz for 2 loops, 53 Hz for 3 loops, 48 Hz for 4 loops, and 43 Hz for 5 loops. Image 1 shows the graph of tension/square of the wavelength graph. On the x-axis, lies the 𝜌𝜆 2 which is linear mass density * wavelength^2. On the y-axis lies the tension (mN). The slope in the graph represents 𝑓 2. The lab results indicate that the frequency gets lower as there are more loops. There seem to be no significant errors because the measurements and calculations are correct.

The conclusion we have derived from the lab was that there is a relationship between frequency, tension, wavelength, and speed. Every loop found was basically half of the loop before them as shown above. The same thing basically happens for wavelength. Wavelength has basically the same happen. Each time a extra loop was added, the wavelength was basically divided by 2. Finally, the frequency went lower starting at 1 loop, the frequency was 55. for loop 2 it was 54, for loop 3 it was 53, for loop 4 it was 48 hz, and lastly for loop 5 it was 43hz. Overall, this lab shows that more tension makes a higher frequency, wavelength, and speed.

From your measurements, compute the wavelength of each standing wave pattern. a. For 1 loop, the wavelength came out to be 2m, for 2 loops, it was 1m, for 3 loops it was 0 for 4 loops it was 0, and for 5 loops it was 0.
Explain why this particular graph is appropriate for this experiment. From your graph determine the frequency of vibration of the wave. Compare this with the value of the frequency based on the fact that wall current is AC 60 Hz. a. This graph is correct because the tension gets lower as we make more loops, causing the 𝜌𝜆 2 value to get lower. So eventually, the frequency of one loop will be the highest, showing a positive relationship. The frequency we’ve got out of this experiment is not so different compared to 60 Hz.
By shaking the string, the vibrator produces waves that travel along the string. What is the speed of the waves? Explain how moving waves produce the stationary pattern observed. a. A standing wave is a combination of 2 waves which are moving in opposite direction but have very similar frequency, so they act as the same wave. The imposition of the two waves act as 1 wave from this effect.
Multiple Choice

Course : General Physics Laboratory I (PHYS 201L)

University : university of south carolina.

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