Question

The shortest pipe in a particular organ is 1.37 m.

(a)

Determine the frequency (in Hz) of the seventh harmonic (at 0°C) if the pipe is closed at one end.

Hz

(b)

Determine the frequency (in Hz) of the seventh harmonic (at 0°C) if the pipe is open at both ends.

(c)

Determine these frequencies (in Hz) at 20.0°C.

pipe | frequency (Hz) |
---|---|

closed | |

open |

Answer #1

**given**

**L = 1.37 m**

**a) at 0 degrees Celsius speed of sound, v = 331
m/s**

**for a closed pipe,**

**7th harmonic, f7 = 7*v/((4*L)**

**= 7*331/(4*1.37)**

**= 423 Hz
<<<<<<------------------Answer**

**b)**

**for an open pipe,**

**7th harmonic, f7 = 7*v/((2*L)**

**= 7*331/(2*1.37)**

**= 846 Hz
<<<<<<------------------Answer**

**c) at 20 degrees celius, v = 331 + 0.6*20 = 343
m/s**

**for a closed pipe,**

**7th harmonic, f7 = 7*v/((4*L)**

**= 7*343/(4*1.37)**

**= 438 Hz
<<<<<<------------------Answer**

**for an open pipe,**

**7th harmonic, f7 = 7*v/((2*L)**

**= 7*343/(2*1.37)**

**= 876 Hz
<<<<<<------------------Answer**

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