PROBLEM 3.1 - STANDING WAVES ON A STRING You want to study the propagation of a progressive sinusoidal mechanical wave on a string, using a vibrator that oscillates a blade to which a string is attached. When the wave arrives at the fixed end, it undergoes a hard reflection and returns on itself, causing the addition of two wave functions of the same frequency and amplitude, but of equal and opposite velocity. Under certain conditions, the superposition of these two waves can give rise to a standing wave. Establish the relevant theoretical model: Part A: Write an equation that relates the square of the velocity of propagation of a wave in a string to the tension in the string. Draw the graph of v2 as a function of tension F. Is this graph linear? If so, what does its slope represent? Part B : Establish the physical model (equation) that relates string length, frequency, suspended mass, mode number and linear density of the string. Choose which of string length and frequency will be the independent variable during part B of the experiment (the other will be the dependent variable). Both choices are possible. The aim of the experiment is to determine the linear mass of the string by performing a linear regression on our data. Choose the x and y axis on your graph based on the equation you've obtained, so that the graph is linear. Indicate what the slope and y-intercept of this graph represent.
PROBLEM 3.1 - STANDING WAVES ON A STRING
You want to study the propagation of a progressive sinusoidal mechanical wave on a string, using a vibrator that oscillates a blade to which a string is attached. When the wave arrives at the fixed end, it undergoes a hard reflection and returns on itself, causing the addition of two wave functions of the same frequency and amplitude, but of equal and opposite velocity. Under certain conditions, the superposition of these two waves can give rise to a standing wave.
Establish the relevant theoretical model:
Part A:
Write an equation that relates the square of the velocity of propagation of a wave in a string to the tension in the string. Draw the graph of v2 as a function of tension F. Is this graph linear? If so, what does its slope represent?
Part B :
Establish the physical model (equation) that relates string length, frequency, suspended mass, mode number and linear density of the string.
Choose which of string length and frequency will be the independent variable during part B of the experiment (the other will be the dependent variable). Both choices are possible.
The aim of the experiment is to determine the linear mass of the string by performing a linear regression on our data. Choose the x and y axis on your graph based on the equation you've obtained, so that the graph is linear. Indicate what the slope and y-intercept of this graph represent.
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