Explanation 1) Concept: By using the formula for resonant frequency f for the pipe in which one end is open and other is closed, and for the pipe in which both ends are open, we can find the corresponding frequencies in each pipe. Comparing these frequencies with the frequency of the string, we can find the pipe in which cause resonance by the sound produced by the string and the oscillation mode that the resonating sound will set up. 2) Formula: i) The resonant frequency f for the pipe in which one end is open and other is closed is f = n v 4 L Where, n = 1,3 , 5 , … . ii) The resonant frequency f for the pipe in which both ends are open is f = n v 2 L Where, n = 1,2 , 3 , … 3) Given: i) The length of the pipe a is L ii) The length of the pipe b is 2 L . iii) The length of the pipe c is L 2 iv) The length of the pipe d is L 2 v) The speed of wave on the string equals to the speed of sound. vi) The fundamental mode n = 1 of oscillation is set up on the string. 4) Calculations: We know that the resonant frequency f for the pipe in which one end is open and other is closed is given by, f = v λ Where v is the speed of sound and λ is the wavelength λ = 4 L n Where L is the length of the pipe and n = 1,3 , 5 , … . For fundamental mode n = 1 Therefore, the resonant frequency is given by f = v 4 L Also, we know that the resonant frequency f for pipe in which both ends are open is given by f = v λ Where v is the speed of sound and λ is the wavelength λ = 2 L n Where L is the length of the pipe and n = 1,2 , 3 , … . For fundamental mode n = 1 Therefore, the resonant frequency is given by f = v 2 L Let, f a , f b , f c and f d be the frequencies in pipe a, b, c and d respectively

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ISBN: 9781118230725

Author: David Halliday, Robert Resnick, Jearl Walker

Publisher: Wiley, John & Sons, Incorporated

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Equation of Waves

Wave is an oscillation or disturbance traveling in a medium. It performs the transportation of energy but does not carry any matter. This motion of waves will transport fuel in a medium without permanent transfer of mass (particle).

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Chapter 17, Problem 10Q

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In which pipe will the sound produced by the string cause resonance and the type of oscillation mode that the resonating sound will set up.

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Chapter 17 Solutions

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To find In which pipe will the sound produced by the string cause resonance and the type of oscillation mode that the resonating sound will set up.

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In which pipe will the sound produced by the string cause resonance and the type of oscillation mode that the resonating sound will set up.