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EXAMINATIONS OF May2005

Code and Name of Course FE30B The Technology of teh SteelpanPaper:

Date and Time: Duration: 3 Hours

INSTRUCTIONS TO CANDIDATES: This paper has 3 pages and 5 questions.

Answer all questions

Q1 / The following signal sequence was sampled at 10kHz.
x(n)={0, .5, 1, 0.6, 0.1, -0.5, -0.5, -0.01}
(a)Determine the Discrete Fourier Transform assuming a uniform window.
(b)Plot the Power Spectral Density and estimate the total signal power.
(c)What is the frequency resolution? How can it be improved? What would you recommend as the worst-case frequency resolution for sampling of a low-C tenor steel pan and why?
(d)What is a Hamming window and why is it often applied in the Fourier analysis of sound samples? / 10 marks
2 marks
4 marks
4 marks
Q2 / a)Describe the method of making drums used for steelpans and the manual, conventional method of making the pan, explaining the purpose of sinking, grooving, firing and chrome plating. As part of your answer draw a rough sketch of the profile of a sunken tenor pan indicating the thickness variation from the rim to the bottom and the grain shape variation.
b)Describe the layout and structure of the notes of a tenor pan in relation to the note frequencies (fundamental and partials). Candidates need only describe the relationship between any group of three pairs of adjacent notes from the rim to the middle of the pan. / 12marks
8 marks
Q3 / (a)How does carbon content affect the properties of the steel used for making steelpans?
(b)Describe the phenomenon of strain aging and explain why the conventional method of firing the pan results in a relatively uniform hardness of the playing area.
(c)Describe a method that has been used for hardening steelpans that does not depend on carbon content.
(d)Describe another surface heat treatment (other than (c) above) that can be used to harden the pan. / 4 marks
6 marks
5 marks
5 marks
Q4 / Figure Q4 shows laser interferograms of the modal patterns for a low-C tenor steelpan made by tuner Bertram Kellman. The dark ringed areas define the antinodal areas for each modal pattern; the number of rings indicate the relative strength of the mode. For this measurement, the D4 note was excited using sinusoidal signals at the frequencies shown. Only the D4 note was excited.
(a)Explain the shape and location of the various patterns observed on each of the D4, A4, D5 and A5 notes at each excitation frequency. Be sure to name the various modes using the designation (n,m), where n is the number of radial nodal lines and m the number of circumferential nodal lines.
(b)Do these frequencies correspond with those expected for a perfectly tuned instrument? Explain. / 12 marks
8 marks
D4 excited at 587Hz / D4 excited at 888Hz

Figure Q4

Q5 / (a)The major distinguishing aspect of the steelpan as a musical instrument is the non-linear dynamics of the vibrating metal shells that constitute the notes. Discuss qualitatively in so far as it relates to tonal structure, the main aspects of this dynamics in respect of
(i)modal interactions and energy transfers among the first three tuned modes on a note, and,
(ii)mode localisation and the modulations on the tones of the sounding note.
(b)Explain
(i)why the quadratic coupling factor (112) between the first and second mode and
(ii)why the detuning parameter (1) for the second mode are the main dynamical parameters on the steelpan.
As an aid to your discussion, you are given that 1=1-22, where 1and 2 are the first and second modal frequencies respectively, and where  is a factor derived from the note shape and its spatial derivative, H is the rise of the note, h is the note thickness and  is Poisson ratio for the steel material forming the panface. / 5 marks
5 marks
5 marks
5 marks

END OF QUESTION PAPER

The University of the West IndiesCourse Code2000-07-31

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INSTRUCTIONS: Each page must be signed by the Examiners and where applicable, the University Examiner and/or the External Examiner. Where the examination does not require a University examiner, he form must be signed by the First and Second Examiners. Completed forms should be handed to the Assistant Registrar (Examinations). The EXTERNAL EXAMINER is requested to sign the draft paper and return it with comments, if any, (on a separate sheet) to the Assistant Registrar (Examinations).

First Examiner / University Examiner
Second Examiner / External Examiner (where / applicable)
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