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Q. No.Two strings \((A,B)\) having linear densities \(\mu_A = 2\times 10^{-4}~\text{kg/m}\) and \(\mu_B = 4\times 10^{-4}~\text{kg/m}\) and lengths \(L_A =2.5~\text{m}\) and \(L_B = 1.5~\text{m}\) respectively are joined. Free ends of \(A\) and \(B\) are tied to two rigid supports \(C\) and \(D\), respectively creating a tension of \(500~\text{N}\) in the wire. Two identical pulses, sent from \(C\) and \(D\) ends, take time \(t_1\) and \(t_2\), respectively, to reach the joint. The ratio \(\dfrac{t_1}{t_2}\) is:
1. \(1.08\)
2. \(1.90\)
3. \(1.67\)
4. \(1.18\)
1. \(1.08\)
2. \(1.90\)
3. \(1.67\)
4. \(1.18\)
Subtopic: Speed of Sound |
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The velocity of sound in air is doubled when the temperature is raised from \(0^{\circ}\text{C}\) to \(\alpha^{\circ}\text{C}\). The value of \(\alpha\) is:
1. \(700\)
2. \(819\)
3. \(500\)
4. \(600\)
1. \(700\)
2. \(819\)
3. \(500\)
4. \(600\)
Subtopic: Speed of Sound |
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The speed of a longitudinal wave in a metallic bar is \(400~\text{m/s}\). If the density and Young's modulus of the bar material are increased by \(0.5\%\) and \(1\%\) respectively then the speed of the wave is changed approximately to: (in m/s)
1. \(399\)
2. \(398\)
3. \(402\)
4. \(401\)
1. \(399\)
2. \(398\)
3. \(402\)
4. \(401\)
Subtopic: Speed of Sound |
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Consider sound waves travelling through ideal gases \(\mathrm{He},\) \(\mathrm{CH_4},\) and \(\mathrm{CO_2.}\) Assume that all vibrational degrees of freedom are frozen (inactive), and that all the gases have the same value of \(\dfrac{P}{\rho},\) where \(P\) is the pressure and \(\rho\) is the density. The ratio of the speeds of sound in the gases, \(v_\mathrm{He}: v_\mathrm{CH_4} : v_\mathrm{CO_2},\) is:
| 1. | \(\sqrt{\dfrac{7}{5}}: \sqrt{\dfrac{5}{3}}: \sqrt{\dfrac{4}{3}}\) | 2. | \(\sqrt{\dfrac{5}{3}}: \sqrt{\dfrac{4}{3}}: \sqrt{\dfrac{7}{5}}\) |
| 3. | \(\sqrt{\dfrac{4}{3}}: \sqrt{\dfrac{5}{3}}: \sqrt{\dfrac{7}{5}}\) | 4. | \(\sqrt{\dfrac{5}{3}}: \sqrt{\dfrac{4}{3}}: \sqrt{\dfrac{4}{3}}\) |
Subtopic: Speed of Sound |
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Given below are two statements; one is labelled as Assertion A and the other is labelled as Reason
In the light of the above statements, choose the most appropriate answer from the options given below:
| Assertion (A): | A sound wave has a higher speed in solids than gases. |
| Reason (R): | Gases have a higher value of Bulk modulus than solids. |
In the light of the above statements, choose the most appropriate answer from the options given below:
| 1. | (A) is true but (R) is false |
| 2. | Both (A) and (R) are true and (R) is the correct explanation of (A) |
| 3. | (A) is false but (R) is true |
| 4. | Both (A) and (R) are true but (R) is not the correct explanation of (A) |
Subtopic: Speed of Sound |
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For a medium, it is given that: Young’s modulus \(=3.2 \times 10^{10}\) N/m2, density \(=8000\) kg/m3. What is the speed of sound in this medium?
1. \(1000\) m/s
2. \(2000\) m/s
3. \(500\) m/s
4. \(4000\) m/s
1. \(1000\) m/s
2. \(2000\) m/s
3. \(500\) m/s
4. \(4000\) m/s
Subtopic: Speed of Sound |
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Sound travels in a mixture of two moles of helium and \(n\) moles of hydrogen. If RMS speed of gas molecules in the mixture is \(\sqrt 2\) times the speed of sound, then the value of \(n\) will be:
1. \(1\)
2. \(2\)
3. \(3\)
4. \(4\)
1. \(1\)
2. \(2\)
3. \(3\)
4. \(4\)
Subtopic: Speed of Sound |
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A resonance tube is old and has a jagged end. It is still used in the laboratory to determine the velocity of sound in air. A tuning fork of frequency \(\mathrm{512 ~Hz}\) produces first resonance when the tube is filled with water to a mark \(\mathrm{11 ~cm}\) below a reference mark, near the open end of the tube. The experiment is repeated with another fork of frequency \(\mathrm{256 ~Hz}\) which produces first resonance when water reaches a mark \(\mathrm{27 ~cm}\) below the reference mark. The velocity of sound in air, obtained in the experiment, is close to:
1. \(\mathrm{322~ms^{-1}}\)
2. \(\mathrm{341~ms^{-1}}\)
3. \(\mathrm{335~ms^{-1}}\)
4. \(\mathrm{328~ms^{-1}}\)
1. \(\mathrm{322~ms^{-1}}\)
2. \(\mathrm{341~ms^{-1}}\)
3. \(\mathrm{335~ms^{-1}}\)
4. \(\mathrm{328~ms^{-1}}\)
Subtopic: Speed of Sound |
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The pressure wave \(P=0.01 \sin (1000 t-3 x) ~\text{Nm}^{-2},\) corresponds to the sound produced by a vibrating blade on a day when the atmospheric temperature is \(0^\circ \text{C}.\) On some other day, when the temperature is \(T,\) the speed of sound produced by the same blade and at the same frequency is found to be \(336~\text{m} \text{s}^{-1}.\) The approximate value of \(T\) is:
1. \( 4^{\circ} \text{C} \)
2. \(12^{\circ} \text{C} \)
3. \(11^{\circ} \text{C} \)
4. \(15^{\circ} \text{C} \)
Subtopic: Speed of Sound |
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