Open Question
(II) A space probe enters the thin atmosphere of a planet where the speed of sound is only about 55 m/s .
(b) What is the angle of the shock wave relative to the direction of motion?
18. Waves & Sound
Standing Sound Waves
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The fundamental frequency of your closed organ pipe is 200 Hz. The second overtone of this pipe has the same frequency as the 3rd harmonic of an open pipe. What is the length of this open pipe?
A
0.85 m
B
0.51 m
C
0.69 m
D
0.43
Verified step by step guidance1
Understand that a closed organ pipe supports only odd harmonics. The fundamental frequency is the first harmonic, so the second overtone is the 5th harmonic.
For a closed pipe, the nth harmonic frequency is given by \( f_n = n \times f_1 \), where \( f_1 \) is the fundamental frequency. Therefore, the frequency of the 5th harmonic is \( 5 \times 200 \text{ Hz} = 1000 \text{ Hz} \).
Recognize that the 3rd harmonic of an open pipe is given by \( f_3 = 3 \times \frac{v}{2L} \), where \( v \) is the speed of sound and \( L \) is the length of the pipe. Set this equal to 1000 Hz.
Solve for the length \( L \) of the open pipe using the equation \( 3 \times \frac{v}{2L} = 1000 \text{ Hz} \). Assume the speed of sound \( v \) is approximately 343 m/s.
Rearrange the equation to find \( L = \frac{3 \times 343}{2 \times 1000} \) and simplify to find the length of the open pipe.
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