STANDING WAVES IN STRINGS AIM: To study the relationship between the tension (st
ID: 2268857 • Letter: S
Question
STANDING WAVES IN STRINGS AIM: To study the relationship between the tension (stretching force) and wavelength in a vibrating string and to determine the tension on a string by means of standing waves. APPARATUS: Vibrator, string, balance, meter string, hanger, masses, and pulley BACKGROUND AND THEORY When a uniform cord is subjected to a stretching force and oscillates at one end, a transverse wave travels down the string. That is, the motion of any particle of the cord is at right angles or transverse to the direction of propagation of the wave. [Another kind of wave is longitudinal wave in which the motion of the particle is along the direction of propagation of the wave.] In this experiment, we will study transverse waves in a regular succession of crests and troughs. As a further review of the fundamental characteristics of wave motion, we shall first define some of the quantities related to waves Amplitude, A: The maximum displacement with respect to the undisturbed string Period, T: The time required for the wave to travel between two successive crests or troughs. wavelength, : The distance between two successive troughs or crests (or the distance traveled in one period T. Phase velocity, v: The distance traveled per unit time, v = /T = . or =v/ f For a stretched string, the velocity y of a transverse wave is related to the stretching force F by the following equation: v=JFju where is the mass per unit length (m/l.) of the string. Combining equations (1) and (2), one obtains: OR F1 = If we plot the wave length versus the inverse of the frequency, lf, we will obtain a straight line graph. The slope of this graph is given by F/ , which is the wave speed on the string. Frorn this, we can thus find the fixed tension F from Equation (2),Explanation / Answer
From the given graph, the slope is
m = 0.0279
linear mass density is
lambda = m/L = 0.7/2 = 0.35kg/m
The slope of lambda vs (1/f) graph is
F/lambda = slope^2 = 0.0279^2
F = 0.0279^2*0.35 = 2.73*10-4 N
b) the slope is equal to the velocity so v = 0.0279m/s
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