Exploring Fundamental Vibrations: Plotting Tensions and Lengths on a String

In summary, the conversation involves a prelab question about plotting a graph with applied tensions and resultant length for a vibrating string in the fundamental mode. The formula for the relationship between tension and length is given, and the individual is considering using a linear function to plot the data and finding the gradient to calculate the linear mass density and frequency. It is noted that the data may not fall on a straight line, and the individual is advised to anticipate a non-zero value for the y-intercept.
  • #1
bennyq
23
0

Homework Statement


This is a prelab question which I hope for some confirmation I'm thinking right.
A vibrating string is vibrating in the fundamental mode. The question is to plot a graph with a succession of applied tensions T on the x-axis and the resultant length L of the fundamental vibration mode on the y-axis


Homework Equations



Formula I have is L^2 = T/4μƒ^2

The Attempt at a Solution


Im thinking that all its asking is to plot a function like y=mx+c where 1/4μƒ^2 is the gradient?

Something of the sort, then ill go on to calculate the linear mass density (μ), do some calculations plot L^2 against T and find this gradient and find the frequency...

Oh and sid
 
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  • #2
You will notice from the formula that L(T) is not a straight line.
To get a line you want to plot L^2 vs T ... you will expect the data to fall on a line like
##L^2 = mT + c## ... so you have that right. Use the data to find m and c, compare with the theory.

You may want to anticipate the possibility (quite likely) that your data has a value of c that is non-zero.
 

What are standing waves on a string?

Standing waves on a string, also known as stationary waves, are a type of wave that occurs when two waves of the same frequency and amplitude travel in opposite directions on a string and interfere with each other. This results in the formation of nodes and antinodes, which are points of maximum and minimum amplitude, respectively.

What factors affect the formation of standing waves on a string?

The formation of standing waves on a string is affected by the tension of the string, the length of the string, and the frequency of the waves. The greater the tension, the shorter the wavelength and the higher the frequency needed for standing waves to form. Similarly, a longer string will require a lower frequency for standing waves to occur.

What is the difference between the fundamental frequency and harmonics in standing waves on a string?

The fundamental frequency is the lowest frequency at which standing waves can form on a string. Harmonics, also known as overtones, are frequencies that are integer multiples of the fundamental frequency. For example, the second harmonic has a frequency twice that of the fundamental frequency.

How do standing waves on a string relate to musical instruments?

Standing waves on a string are what allow musical instruments, such as guitars and violins, to produce sound. The strings of these instruments vibrate at certain frequencies, creating standing waves and producing different musical notes.

What are some real-world applications of standing waves on a string?

Standing waves on a string have various practical applications, such as in musical instruments, telecommunications, and medical imaging. In telecommunications, standing waves are used to transmit signals through wires and cables. In medical imaging, standing waves are used in ultrasound technology to produce images of internal body structures.

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