Question

3. What will be the fundamental frequency and first overtone for a 26-сm long organ pipe if it is a. open at both ends? b. closed at one end? 4. You observe that "demented ice cream truck phenomenon one day. When the truck is stationary nearby, it is playing a song of mostly 550 Hz. When it pulls away you observe a frequency of 543 Hz (more than enough to sound 'out of tune'). How fast did it pull away from you?

Answer 1

Problem - 3

Length of the organ pipe, L = 26 cm

                                             = 0.26 m

    Velocity of sound, V = 343 m/s

(a)

    Frequency, f = n V / 2 L , for n = 1, 2, 3 , ...( pipe , two open ends )
                                           where n = harmonic number

    Fundamental frequency, f = ( 1) * ( 343 ) / 2 *( 0.26 ) = 659.6 Hz

    Frequency of first overtone = 2f = 1319.23Hz

    Frequency of second overtone = 3f = 1978.8Hz

    Frequency of third overtone = 4f = 2638.4 Hz

(b)

   Frequency, f = n V / 4 L , for n = 1, 3, 5 , ... (pipe, one open end )
                                           where n = harmonic number

    Fundamental frequency, f = ( 1) * ( 343 ) / 4 *( 0.26 ) = 329.8 Hz

   Frequency of first overtone = 3f = 989.4 Hz

    Frequency of second overtone = 5f = 1649 Hz

    Frequency of third overtone = 7f = 2308.6 Hz