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InterviewSolution
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(i) A person hums in a wall and finds strong resonance at frequencies `60 Hz, 100Hz` and `140 Hz`. What is the fundamental frequency of the well? Explain? How deep is the wall ? (velocity of sound `= 344 m//`). (ii) A violin string `33cm` long vibrates at a fundamental frequency of `440 Hz`. Where shold a finger be pressed on the string board so that its decreased length causes it to vibrate in its fundamental mode at five fourth of its original frequnency. |
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Answer» Correct Answer - (i) fundamental frequercy `n = 20 Hz`, depth of the weil `= 4.3`, (ii) at `26.4 cm` from the end. (i) The well can be considered as an organ pipe closed at one end and open at the other. At the fundamental mode, `lambda//4 = l` (depth of the well in this case). The given frequencies happen to be `3rd, 5th` & `7th` harmonics of the fundamental frequency `n = 20 Hz`. Now use `v = nlambda` so as to obtain depth of the well `= 4.3 m`. (ii) Use the law of vibrating string ni `=` constant. To have the frequency `5//4` th of original, the length requireed `4//5` of `33cm`. Thus, the finger must be pressed at a point will divid the length of the string in a ratio `1:4` is at `26.4 cm` from the end. |
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