PHYS 223 - Lab 9 (1)

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Mohammad Malik PHYS 223-06 March 30, 2023 Lab #9 Partner: Olivia Dobson Transverse Wave Motion Introduction Oscillatory motion is defined as waves traveling up and down on a string. This wave motion is known as transverse wave motion, which is when a wave is vibrating at right angles to the direction of its propagation. The waves will endure a 180-degree phase change when the wave travels to the end of the string and then is reflected up the string. While waves are oscillating, destructive interference could occur when the crest of one wave meets the trough of another due to the waves being reflected at both ends, and the result is a lower total amplitude

unless the length of the string is equal to an integer number of half wavelengths. L = nλ/2 is the equation used where L is the length of the string, n is the integer number of loops observed, and λ is the wavelength. Objective The objective of this lab was to conduct an experiment on the relationship between transverse wave motion, tension, and frequency. This was achieved by utilizing an oscillator machine and a string tied to both ends. One end being the oscillator machine and the other being a pulley system where there is a hanger hanging on the end of the string applying tension by putting mass on a hanger and is acted upon by force due to gravity. The equations listed in the introduction were also utilized to determine the slope of the graph between ^2 and the force of tension. Experimental Data # loops M T λ λ 2 11 200g 1.96 N 0.329 0.108 9 300g 3.92 N 0.465 0.216 6 650g 5.88 N 0.57 0.325

1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 f(x) = 0.06 x − 0 Graph 1 Tension (N) ʎ2 L = 2.3 m Length of string = 281.5 cm = 2.815m Mass of String = 5.2g = 0.0052kg μ = 0.001847 kg/m f = 99.0 Hz T = mg T = 0.2kg(9.8) = 1.96 N 0.4kg(9.8) = 3.92 N 0.6kg(9.8) = 5.88 N ʎ ¿ 1 f √ T μ = ¿ 1 99 Hz √ 1.96 N 0.001847 kg / m = 0.329 1 99 Hz √ 3.92 N 0.001847 kg / m = 0.465 1 99 Hz √ 5.88 N 0.001847 kg / m = 0.57

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Questions & Analysis 1 . Plot the tension in the string against λ2. From this straight line calculate f. Slope: s = 1 f 2 ( μ ) => f = √ sμ sμ = ¿ √ 0.0554 ( 0.001847 ) 0.0554 ( 0.001847 ) = 98.86 Hz 2. Calculate the percentage error for f. % error = | experimental − actual actual | x 100% = ¿ | 98.86 − 99.0 99.0 | x 100% = 0.14% 3. What general effect does increasing the tension have upon a vibrating string? Increasing the tension of a string generally causes the frequency of the string to increase. 4. Is there a true node at the vibrator end of the string? Explain. No. Since one end of the string is attached to the motor, the segment connected to the motor must be neglected, because the motion at the motor prevents a true node from forming at that end . 5. All the strings on a violin, cello, and guitar are the same length. What differences do they have which give them different frequencies? What other way can the frequency be Changed? The tension in the strings can explain why they all have different frequencies. The higher the tension the higher the frequency and you adjust the tensions of the strings differently for each instrument. Another way the frequency can be changed is the speed. All waves in a string travel at the same speed, so waves with different wavelengths have different frequencies. 6. A copper wire one meter long weighing 0.02 grams per cm. vibrates in three segments when under a tension of 280 grams. What is the frequency of this vibration?

L = 1 m = 100 cm T = 280 g = 0.02 g/cm 𝜇 = 2 / = 2(100)/3 = 66.67 𝜆 𝐿 𝑛 = √ / = √ (280 980/0.02) = 3704.05 /s 𝑉 𝑇 𝜇 ∗ 𝑐𝑚 = 𝑉 𝑓𝜆 = = 3704.05 66.67 = 55.56 z 𝑓 𝑉 𝜆 𝐻 Discussion & Conclusions I n conclusion, by utilizing an oscillator machine and a string tied to the machine and a weight by a pulley system, the relationship between transverse wave motion, tension, and frequency was determined. The force of tension and wavelength were calculated for each trial conducted. From there, a graph was created by graphing 2 against the force of tension. The graph formed a near linear relationship between the tension on the string and the frequency. Comparing our velocity to the experimental value gave us our error percentage. The % Error of frequency that was calculated was 0.14%. Although it is a small % Error, which could have been caused by a reading error of the string and its nodes. Despite the possible errors experienced, it was successfully proven that there is a relationship between tension and frequency.

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