Phys2426 LAB REPORT FORM STANDING WAVES ON A STRETCHED STRING Part A: Measuring

Question

Phys2426 LAB REPORT FORM STANDING WAVES ON A STRETCHED STRING Part A: Measuring the Linear Mass Density of String Data Table 1 m (kg) mass of string -me ( kgm) linear mass density total length of string Go S8 1.49m Part B: Predicting the Harmonic Frequencies Data Table 2 Length of String, L-0.8 m wavelength, ,-2L = 1.6 m Hanging (N) (Hz) (Hz) | (112) | (Hz) (Hz | (Hz Mass | Tension | (mas) 2103 20 35os 0.070 10.58s |,3.26| 8.29·6Sel2487|3316|Y1HS 0.120 |23-42/3513|Ysg%gs | 18.74 | 11-71 ·2-9.8 mw 0.140 |137 is from Data Table 1 Part C: Measuring First to Sixth Harmonics Data Table 3 1 " S. 7-3S. M (kg) %Diff |(is for 0.050 0.070 NO 123 2 36.7 490 61.9 273 12 SS3 8.3 0.120 0.140 3.8

Explanation / Answer

wave are the means by which energy is transported across the string.

The fundamental vibrational mode of a stretched string is such that the wavelength is twice the length of the string.

The frequency of the wave is directly proportional to the tension across the string and inversely proportional to the mass per unit length across the string.

The string will also vibrate in all harmonics of the fundamental. Each of these harmonics will form a standing wave on the string.

For the strings of finite stiffness, the harmonic frequencies will depart progressively from the mathematical harmoncis.

The higher harmonics will be integral and half integral multiples of the length of the string.

tension across the string and mass per unit length (linear mass density) play a very important role in deciding the fundamental frequency.

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