Standing waves in strings and organ pipes, harmonics
- A pipe open at both ends has a fundamental frequency f in air. The pipe is now dipped vertically in a water drum to half of its length. The fundamental frequency of the air column is now equal to : Answer: 2. f Key idea: an open pipe of length L has fundamental f=v/2L ; a pipe closed at one end of length l has fundamental v/4l . Dipping... 1
- The ratio of frequencies of fundamental harmonic produced by an open pipe to that of closed pipe having the same length is : Answer: 3. 2 : 1 Fundamental frequency of an open pipe: f_o=v/2L . For a closed pipe: f_c=v/4L . f_o/f_c=4L/2L=2:1 . The answer is 2 : 1. 1
- The fundamental frequency in an open organ pipe is equal to the third harmonic of a closed organ pipe. If the length of the closed organ pipe is 20 cm, the length of the open organ pipe is Answer: 1. 13.2 cm Closed pipe: odd harmonics only, f_n=nv/4L . Third harmonic: f=3v/4× 20 . Open pipe fundamental: f₁=v/2L' . Equating: v/2... 1
- The two nearest harmonics of a tube closed at one end and open at other end are 220 Hz and 260 Hz. What is the fundamental frequency of the system ? Answer: 1. 20 Hz Key idea: a tube closed at one end has only odd harmonics: f₀,3f₀,5f₀,dots . Consecutive harmonics differ by 2f₀ . 260-220=... 1
- The second overtone of an open organ pipe has the same frequency as the first overtone of a closed pipe L metre long. The length of the open pipe will be Answer: 1. 2L Compare the frequencies using v as the speed of sound. Open pipe of length l : harmonics nv/2l ; the second overtone is the 3r... 1
- An air column, closed at one end and open at the other, resonates with a tuning fork when the smallest length of the column is 50 cm. The next larger length of the column resonating with the same tuning fork is : Answer: 3. 150 cm Key idea: a closed pipe resonates at odd multiples of λ/4 : lengths L, 3L, 5L,dots Smallest length =λ/4=50 cm. The next re... 1