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JEE Advanced 2023 Paper 1 · Physics · Waves and Sound · easy

Sound travels at speed v in the air of each pipe described in List-I; end effects are negligible. List-II gives frequencies in units of v/L. List-I…

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Sound travels at speed vv in the air of each pipe described in List-I; end effects are negligible. List-II gives frequencies in units of v/Lv/L. Match List-I with List-II.

List-I
(P) Fundamental frequency of a pipe of length L/2L/2 closed at one end
(Q) Beat frequency when the fundamentals of an open pipe of length LL and a closed pipe of length LL sound together
(R) First overtone of a pipe of length LL closed at one end
(S) Second overtone of a pipe of length LL open at both ends

List-II
(1) 14\dfrac14
(2) 12\dfrac12
(3) 34\dfrac34
(4) 11
(5) 32\dfrac32
  1. A. P→2, Q→1, R→3, S→5
  2. B. P→2, Q→1, R→5, S→3
  3. C. P→1, Q→2, R→3, S→5
  4. D. P→2, Q→4, R→3, S→5
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Answer: (A) P→2, Q→1, R→3, S→5

A closed pipe of length ℓ\ell has frequencies (2m+1)v4ℓ(2m+1)\dfrac{v}{4\ell}; an open pipe has mv2ℓm\dfrac{v}{2\ell}. (P) Closed, ℓ=L/2\ell=L/2, fundamental: v4(L/2)=v2L\dfrac{v}{4(L/2)}=\dfrac{v}{2L}, which is (2). (Q) Open fundamental v2L\dfrac{v}{2L}, closed fundamental v4L\dfrac{v}{4L}, beats =v2L−v4L=v4L=\dfrac{v}{2L}-\dfrac{v}{4L}=\dfrac{v}{4L}, which is (1). (R) The first overtone of a closed pipe is the third harmonic, 3v4L\dfrac{3v}{4L}, which is (3). (S) The second overtone of an open pipe is the third harmonic, 3v2L\dfrac{3v}{2L}, which is (5). Item (4) is unused. Thus P→2, Q→1, R→3, S→5.
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Original question written in the JEE Advanced 2023 Paper 1 pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake