We want to relate some percussion natural mode frequencies with notes on the pia

We want to relate some percussion natural mode frequencies with notes on the piano
keyboard.
(a) Write out the frequencies for the first four modes of an ideal free uniform bar
whose first mode is at C4(261.6 Hz). Give the closest note names for these
frequencies and for each mode indicate how well its frequency matches with that
of the corresponding equal-tempered note. (You can consider it to be a good
match if the frequency of a mode is within about 1% of the equal-tempered note
frequency.)
(b) Now do the same for the first 10 modes of an ideal stretched membrane whose
first mode is at C4(261.6 Hz). (ie write out the frequencies note names and
indicate how well the frequencies match the notes.)
Physics 288/489 The Physics of Music Winter 2013 Homework Assignment #7 | Due Wednesday March 13 1. We want to relate some percussion natural mode frequencies with notes on the piano keyboard. (a) Write out the frequencies for the rst four modes of an ideal free uniform bar whose rst mode is at C4 (261.6 Hz). Give the closest note names for these frequencies and for each mode indicate how well its frequency matches with that of the corresponding equal-tempered note. (You can consider it to be a good match if the frequency of a mode is within about 1% of the equal-tempered note frequency.) (b) Now do the same for the rst 10 modes of an ideal stretched membrane whose rst mode is at C4 (261.6 Hz). (ie write out the frequencies note names and indicate how well the frequencies match the notes.) 2. [Based on Musical Acoustics Chapter 9 Exercise 24] Describe the vibration recipe (ie which modes are active) immediately after striking a bar free at both ends (a) precisely at its center (b) nearly at the center (c) well o-center 3. [Musical Acoustics Chapter 9 Exercise 18] Which four of the drumhead modes of Figure 9.16 (the natural modes of a stretched membrane) are shown in Figure 9.17 (the photographs of the rubber membrane)? Give your answers in the order of the sequence of pictures in Figure 9.17 from top to bottom and briey explain the reasoning behind your answer. 4. [Based on Musical Acoustics Chapter 10 Exercise 3] Suppose you have a string of length L = 33 cm on which waves travel at speed vt = 290 m/s. As we have seen the modes of the string can be regarded as standing waves. (a) What is the wavelength 3 of the third mode? (This is the wavelength of the transverse string vibration not of the resulting sound in air.) (b) What is the frequency f3 of the third mode? (c) What note (piano key) does this frequency correspond to? 1
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