Homework Help is Here – Start Your Trial Now!
Science
Advanced Physics
A string of length L and mass M is under a tension F. One end of it is fixed in place at x = 0, while the other end is free to move up and down at x = L. (a) Starting from the standard form of y(x, t) for a harmonic standing wave, derive the wavelength of the normal modes on this string: λn = 4L/n. (b) State clearly, what values of n are allowed. (c) Obtain the normal mode frequencies v in terms of L, M, F and n and write the full wave functions in these terms (for arbitrary amplitude, A). (d) Sketch the first two allowed harmonics, indicating the positions of

A string of length L and mass M is under a tension F. One end of it is fixed in place at x = 0, while the other end is free to move up and down at x = L. (a) Starting from the standard form of y(x, t) for a harmonic standing wave, derive the wavelength of the normal modes on this string: λn = 4L/n. (b) State clearly, what values of n are allowed. (c) Obtain the normal mode frequencies v in terms of L, M, F and n and write the full wave functions in these terms (for arbitrary amplitude, A). (d) Sketch the first two allowed harmonics, indicating the positions of

icon
Related questions
Question
= A string of length L and mass M is under a tension F. One end of it is fixed in place at x = 0, while the other end is free to move up and down at x = L. (a) Starting from the standard form of y(x, t) for a harmonic standing wave, derive the wavelength of the normal modes on this string: 2n :4L/n. (b) State clearly, what values of n are allowed. (c) Obtain the normal mode frequencies v in terms of L, M, F and n and write the full wave functions in these terms (for arbitrary amplitude, A). (d) Sketch the first two allowed harmonics, indicating the positions of all modes and antinodes. (e) With L = 2 m and M = 8 g, the string supports the standing waves 0.03 sin(3.25x) cos(162.5πt) for x and y in metres and t in seconds. Find (i) the value of n for this harmonic; (ii) the tension in the string. y(x, t) =
Transcribed Image Text:= A string of length L and mass M is under a tension F. One end of it is fixed in place at x = 0, while the other end is free to move up and down at x = L. (a) Starting from the standard form of y(x, t) for a harmonic standing wave, derive the wavelength of the normal modes on this string: 2n :4L/n. (b) State clearly, what values of n are allowed. (c) Obtain the normal mode frequencies v in terms of L, M, F and n and write the full wave functions in these terms (for arbitrary amplitude, A). (d) Sketch the first two allowed harmonics, indicating the positions of all modes and antinodes. (e) With L = 2 m and M = 8 g, the string supports the standing waves 0.03 sin(3.25x) cos(162.5πt) for x and y in metres and t in seconds. Find (i) the value of n for this harmonic; (ii) the tension in the string. y(x, t) =
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 6 steps with 35 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer