Answers
Download PDF Document(447k) Printable (300dpi) GIF images:
Page 1(90k), Page 2(122k)

Screen (100dpi) GIF images:
Page 1(18k), Page 2(24k)

Blank Homeworks
Download PDF Document(25k)

Download Word Document(31k)
-- right click (Control + click on Mac)
-- save file
-- open file in MS Word 		Printable (300dpi) GIF images:
Page 1(74k), Page 2(88k)

Screen (100dpi) GIF images:
Page 1(14k), Page 2(17k)

NAME: _______________________, Sect. #_______

Physics 109 Homework # 5
due Monday, October 15, 2001

Formulae: in air v = 340m/s. Open: f1 = v/2L; fn = nf1; Closed: f1 = v/4L

Exercises on pipes:

  1. (a) Find the fundamental frequency and the frequencies of the first two overtones of an open pipe of 60 cm length.

    _________ Hz, __________ Hz, _________Hz.

    (b) if the same pipe is closed at one end, what are the corresponding frequencies?

    _________ Hz, __________ Hz, _________Hz.

  2. (a) Make a graph of the pressure at different instances in an open pipe (left) and in a closed pipe (right) oscillating in the fundamental mode.

    (hint: first mark the pressure nodes by letter N - then draw the curves)
    press
    make a corresponding graph or the air velocity distribution in the pipe. (remember slinky demo - where does it move most, where does it not move at all?)
    air velocity
    (b) make corresponding pressure graphs for the next higher mode.
    press

  3. Between room temperature (20O C) and body temperature (37O C) the speed of sound increases by 10 m/s. A flute has a frequency of 260 Hz when it is cold.
    Find the frequency when the flute is warmed to body temperature by the flutist's breath (hint: use proportions to relate frequencies to speed of sound - what is the ratio of speed of sound at the two temperatures? What is the frequency ratio?)

    f = _____________

Exercises on Fourier Analysis

NOTE: we can usually not figure out the amplitudes of the overtones, but can only find out which are present and what their frequencies are. Thus when you are asked to draw a Fourier spectrum the position of the Fourier components should be in the right place, but the intensity is arbitrary.

4. (a) What might the Fourier spectrum of a closed pipe with fundamental frequency 300 Hz look like?
axes
  		(b) What is the spectrum when the same pipe is open at both ends?
axes
 
5. What might the Fourier spectrum of a 500 Hz violin string look like when it is plucked 1/3 the length from one end? axes