Waves & Sound · JEE Main previous year questions

2024 10 questions

1. Q512024 · 8 Apr 2024 · Shift 1· Numerical answer

   A closed and an open organ pipe have same lengths. If the ratio of frequencies of their seventh overtones is $\left(\frac{a-1}{a}\right)$ then the value of $a$ is ________.

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   Answer: 16

2. Q502024 · 8 Apr 2024 · Shift 2

   A plane progressive wave is given by $y=2\cos 2\pi (330t-x)\mathrm{m}$. The frequency of the wave is :

   1. A.$660\mathrm{Hz}$
   2. B.$340\mathrm{Hz}$
   3. C.$330\mathrm{Hz}$
   4. D.$165\mathrm{Hz}$
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   Answer: C

3. Q502024 · 6 Apr 2024 · Shift 2

   In the given electromagnetic wave ${\mathrm{E}}_y=600\sin (\omega t-\mathrm{k}x){\mathrm{Vm}}^{-1}$, intensity of the associated light beam is (in $W/{\mathrm{m}}^2$) : (Given ${ϵ}_0=9\times 10^{-12}{\mathrm{C}}^2{\mathrm{N}}^{-1}{\mathrm{m}}^{-2}$ )

   1. A.486
   2. B.729
   3. C.243
   4. D.972
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   Answer: A

4. Q582024 · 6 Apr 2024 · Shift 2· Numerical answer

   Two open organ pipes of lengths $60\text{ cm}$ and $90\text{ cm}$ resonate at $6^{\text{th}}$ and $5^{\text{th}}$ harmonics respectively. The difference of frequencies for the given modes is ________ $\text{Hz}$. (Velocity of sound in air $=333\text{ m/s}$)

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   Answer: 740

5. Q422024 · 4 Apr 2024 · Shift 1

   The equation of stationary wave is : $y=2\mathrm{a}\sin \left(\frac{2\pi \mathrm{nt}}{\lambda }\right)\cos \left(\frac{2\pi x}{\lambda }\right)$. Which of the following is NOT correct :

   1. A.The dimensions of $nt$ is $[\mathrm{L}]$
   2. B.The dimensions of $n$ is $[{\mathrm{LT}}^{-1}]$
   3. C.The dimensions of $x$ is $[\mathrm{L}]$
   4. D.The dimensions of $n/\lambda$ is $[\mathrm{T}]$
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   Answer: D

6. Q592024 · 1 Feb 2024 · Shift 1· Numerical answer

   A tuning fork resonates with a sonometer wire of length $1\mathrm{m}$ stretched with a tension of $6\mathrm{N}$. When the tension in the wire is changed to $54\mathrm{N}$, the same tuning fork produces 12 beats per second with it. The frequency of the tuning fork is ____ $\mathrm{Hz}$.

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   Answer: 6

7. Q412024 · 31 Jan 2024 · Shift 1

   The fundamental frequency of a closed organ pipe is equal to the first overtone frequency of an open organ pipe. If length of the open pipe is $60\mathrm{cm}$, the length of the closed pipe will be:

   1. A.15 cm
   2. B.60 cm
   3. C.45 cm
   4. D.30 cm
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   Answer: A

8. Q392024 · 31 Jan 2024 · Shift 2

   The speed of sound in oxygen at S.T.P. will be approximately: (given, $R=8.3\mathrm{J}{\mathrm{K}}^{-1},\gamma =1.4$)

   1. A.341 m/s
   2. B.333 m/s
   3. C.325 m/s
   4. D.315 m/s
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   Answer: D

9. Q562024 · 30 Jan 2024 · Shift 1· Numerical answer

   In a closed organ pipe, the frequency of fundamental note is $30\text{ Hz}$. A certain amount of water is now poured in the organ pipe so that the fundamental frequency is increased to $110\text{ Hz}$. If the organ pipe has a cross-sectional area of $2{\text{ cm}}^2$, the amount of water poured in the organ tube is _________ g. (Take speed of sound in air is $330\text{ m/s}$)

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   Answer: 400

10. Q512024 · 27 Jan 2024 · Shift 2· Numerical answer

    A closed organ pipe $150\text{ cm}$ long gives 7 beats per second with an open organ pipe of length $350\text{ cm}$, both vibrating in fundamental mode. The velocity of sound is _______ $\text{m/s}$.

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    Answer: 294