Question

18, + 03 points i Frenous Answars The shortest pipein a particular organ is 1.41 m (a) Determine the frequency (in Hz) of the ninth harmonic (at 0°C) if the pipe is closed at one end. 548.93 Racall that the pipe is closed at ane end. When standing wave rasonance occurs in a pipe closed at one and, the length of the pipe is an odd integral number of quarter wavelengths. Can you express the wavelength of the traveling wava speed and the frequency of the sound? Use the above information to express the desired frequancy of the sound in terms of the spond of sound and the length of the pipe. Hz (b) Determine the frequency (in Hz) af the ninth harmonic (at 0°C) if the pipe is apen at both ands 504 Recall that the pipe is opan at both ends. When standing wave resonance occurs in a pipe opan at both ands, the length of the pipe is an integral number of half wavelengths. Can you express the wavelength of the traveling waves in the and the frequency of the sound? Use the above information to express the desired frequency of the sound in terms of the speed of sound and the length of the pipe. Hz (C) Datarmina these frequencies (in Hz) at 20.0°C. frequency (Hz) pipe closad 1343 | open Be sure to correct the speed of sound for the temperature. As the temperature increases, does the speed of sound increase or decrease? Review parts (a) and (b) to see if you can take advantage of your previous work Need Help? Readt

Answer 1

a) 9th harmonic,

f9 = 9*v/(4*L)

= 9*331.6/(4*1.41)

= 529.1 Hz

b) f9 = 9*v/(2*L)

= 9*331.6/(2*1.41)

= 1058 Hz

c) at T = 20 C

v = 331.6 + 20*0.6

= 343.6 m/s

for closed pipe,
f9 = 9*v/(4*L)

= 9*343.6/(4*1.41)

= 548.3 Hz

for open pipe,
f9 = 9*v/(2*L)

= 9*343.6/(2*1.41)

= 1096 Hz