Exam 3 Review Pipes Problems Exam 3 Review Problems 1 On a guitar the G string has a fundamental frequency of 196 Hz and a length of 60 cm The guitar player increases the fundamental frequency of the G string by placing a finger on the fingerboard so that the vibrating length becomes shorter What is the vibrating length of this same string to play a an A at 220 Hz b a B at 247 Hz c a C at 262 Hz d a D at 294 Hz e an E at 330 Hz f an F at 349 Hz g another A at 440 Hz h What is the relationship between the A in a at 220 Hz and the A in g at 440 Hz Exam 3 Review Pipes Problems 2 On a guitar the E string is shortened by placing a finger on the fingerboard The length of the untouched E string is 60 cm and its fundamental frequency is 82 Hz a What is the tension in the string if its linear mass density is 6 5 g m b What is the fundamental frequency of this string when it is shortened to i L 53 5 cm ii L 44 7 cm iii L 33 5 cm iv L 29 8 cm v L 25 1 cm vi L 18 8 cm 3 How does the fundamental frequency change when the tension of an 800 Hz string is doubled Exam 3 Review Pipes Problems 4 A string is plucked at L 3 Which partials are present in the sound produced List them and then show on a Fourier spectrum 5 A violin string is 32 5 cm long is tuned to play a tone called D4 297 Hz Where should you place the finger on the fingerboard to play a tone one octave above D4 One fifth above D4 One fourth above D4 Use just tuning for this question Hint Use the scales graphic to find the right ratios 6 If you pluck a string in the middle and then touch it lightly at one third of its length what modes survive Give the number of each mode present Also sketch the Fourier spectra for each step here Exam 3 Review Pipes Problems 7 If you pluck a string at one third of its length and then touch it lightly in the middle what modes survive Give the number of each mode present Also sketch the Fourier spectra for each step here 8 Select the correct answers in the following sentences Standing waves are the result of superposition of two sinusoidal waves of the same different frequency and the same different amplitude traveling in the same opposite directions 9 The flute is an open pipe that plays C4 264 Hz when all finger holes are closed how long is the flute 10 Explain how the frequency of an 80 cm long open pipe changes if you a Change the length from 80 cm to 100 cm Find the frequency for both lengths b Keep the length at 80 cm but close the pipe c Change the diameter of the pipe from 2 cm to 4 cm ignore acoustic length corrections Exam 3 Review Pipes Problems d Increase the air temperature 11 The fundamental frequency of an open pipe is 200 Hz a What is the length of this pipe b How should the length be changed if you want to double the frequency 11 continued c What will the frequency of the original 200 Hz pipe be if one end is closed d Show what the Fourier spectra of the original open pipe and of the closed pipe might look like Open Closed Exam 3 Review Pipes Problems 12 An open organ pipe is 88 cm long and is played in January in an unheated church at a temperature of 5 C When the pipe was tuned to play G3 196 Hz the previous June the temperature was 21 C a What is the frequency this pipe plays in January b Does the pipe sound sharp too high or flat too low in January c By what percent has the frequency changed from June to January 13 Draw the first 5 modes of oscillation of the pressure standing wave in open and a closed pipes Exam 3 Review Scales Problems 14 If you tune A4 to 440 Hz what is the frequency of C4 in just tuning Note C4 has a lower frequency than A4 Use the scales graphic to solve 15 The tempered scale is based on the frequency ratio of two pitches a semitone apart a What is the ratio for a whole tone interval a major second Show your calculation b Show how your calculation of the ratio of frequencies for a tempered major third 16 The D string of a guitar is 60 cm long and tuned to D3 a Where must you place your finger on the fingerboard to play one octave above D3 b What should the length be to play E3 using tempered tuning 17 Complete these major triads C E F A and G B 18 List the advantages and disadvantages of the tempered scale List the advantages and disadvantages of the just scale Exam 3 Review Fourier Analysis Problems 19 Draw the Fourier spectrum of a string plucked from the end and then touched lightly at the midpoint Pluck at L 4 Then touch at L 2 20 Draw an approximate Fourier spectrum that results if you pluck a 100 cm long string with 250 Hz fundamental frequency at a point 33 cm from one end 21 Suppose you have a complicated waveform which represents a periodic oscillation with period 5 ms What does Fourier s theory tell us about representing this complicated waveform in terms of sine waves Draw an approximate Fourier spectrum for this oscillation with the first 5 frequencies