The Third Harmonic of an Organ Pipe of Length L

Multiple Choice

The third harmonic of an organ pipe of length L open at one end has nodes at the closed end, 2L/5 from the closed end, and 4L/5 from the closed end. The open end is an antinode. What expression describes this wave? Take the speed of sound to be 336 m/s, the length of the pipe to be 2.0 m, and let x be the distance from the closed end.

A) A sin[(3.9 m^-1) x] sin[(210 s^-1) t + φ]
B) A cos[(3.9 m^-1) x] sin[(1.3 x 10³ s^-1) t + φ]
C) A cos[(3.9 m^-1) x] cos[(210 s^-1) t + φ]
D) A sin[(3.9 m^-1) x] sin[(1.3 x 10³ s^-1) t + φ]
E) A sin[(0.625 m^-1) x] sin[(4.8 x 10^-3 s^-1) t + φ]