354643
Assertion : The fundamental frequency of an open organ pipe increases as the temperature is increased. Reason : As the temperature increases, the velocity of sound increases more rapidly than length of the pipe
1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Both Assertion and Reason are incorrect.
Explanation:
We know that the fundamental frequency of open organ pipe is given by \(f=\dfrac{v}{2 l}(v-\) velocity of sound). Hence as temperature increases \(v\) increases and therefore \(f\) increases. So assertion and reason are correct and reason supports assertion.
AIIMS - 2011
PHXI15:WAVES
354644
According to Laplace correction, the propagation of sound in gas takes place under
1 Isothermal condition
2 Isobaric condition
3 Isochoric condition
4 Adiabatic condition
Explanation:
Conceptual Question
PHXI15:WAVES
354645
Oxygen is 16 times heavier than hydrogen. Equal volumes of hydrogen and oxygen are mixed. The ratio of speed of sound in the mixture to that in hydrogen is
1 \(\sqrt{\dfrac{1}{8}}\)
2 \(\sqrt{\dfrac{32}{17}}\)
3 \(\sqrt{8}\)
4 \(\sqrt{\dfrac{2}{17}}\)
Explanation:
Density of mixture \(\begin{aligned}& =\rho_{\text {mix }}=\dfrac{V_{o_{2}} \rho_{o_{2}}+V_{H_{2}} \rho_{H_{2}}}{V_{o_{2}}+V_{H_{2}}} \\& =\dfrac{V\left(\rho_{\mathrm{O}_{2}}+\rho_{H_{2}}\right)}{2 V}=\dfrac{\rho_{\mathrm{O}_{2}}+\rho_{H_{2}}}{2}\end{aligned}\) where \({V_{{O_2}}} = {V_{{H_2}}} = V\) \(=\dfrac{\rho_{H_{2}}+16 \rho_{H_{2}}}{2}=8.5 \rho_{H_{2}}\) The velocity is related with density as \(\begin{aligned}& v \alpha \dfrac{1}{\sqrt{\rho}} \\& \Rightarrow \dfrac{v_{\text {mix }}}{v_{H_{2}}}=\sqrt{\dfrac{\rho_{H_{2}}}{\rho_{\text {mix }}}}=\sqrt{\dfrac{\rho_{H_{2}}}{8.5 \rho_{H_{2}}}}=\sqrt{\dfrac{2}{17}}\end{aligned}\)
PHXI15:WAVES
354646
Assertion : Sound travels faster in solids than gases. Reason : Solid possesses greater density than gases.
1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
Explanation:
Sound travels faster in solids due to their higher density , which allows for quicker transmission of mechanical waves through closely packed particles. The reason is also true as it correctly attributes the faster sound propagation in solids to their greater density compared to gases. So option (1) is correct.
PHXI15:WAVES
354647
It takes of 2.0 seconds for a sound wave to travel between two fixed points when the day temperature is \(10^\circ C\). If the temperature rise to \(30^\circ C\) the sound wave travels between the same fixed parts in
1 \(2.0\,{\mkern 1mu} \sec \)
2 \(1.9{\mkern 1mu} \,\sec \)
3 \(2.2\,{\mkern 1mu} \sec \)
4 \(2.1{\mkern 1mu} \,\sec \)
Explanation:
Suppose the distance between two fixed points is \(d\) then \(t=\dfrac{d}{v}\) also \(v \propto \sqrt{T}=\dfrac{t_{1}}{t_{2}}=\dfrac{v_{2}}{v_{1}}=\sqrt{\dfrac{T_{2}}{T_{1}}}\) \(\Rightarrow \dfrac{2}{t_{2}}=\sqrt{\dfrac{303}{283}} \Rightarrow t_{2}=1.9 \mathrm{sec}\).
354643
Assertion : The fundamental frequency of an open organ pipe increases as the temperature is increased. Reason : As the temperature increases, the velocity of sound increases more rapidly than length of the pipe
1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Both Assertion and Reason are incorrect.
Explanation:
We know that the fundamental frequency of open organ pipe is given by \(f=\dfrac{v}{2 l}(v-\) velocity of sound). Hence as temperature increases \(v\) increases and therefore \(f\) increases. So assertion and reason are correct and reason supports assertion.
AIIMS - 2011
PHXI15:WAVES
354644
According to Laplace correction, the propagation of sound in gas takes place under
1 Isothermal condition
2 Isobaric condition
3 Isochoric condition
4 Adiabatic condition
Explanation:
Conceptual Question
PHXI15:WAVES
354645
Oxygen is 16 times heavier than hydrogen. Equal volumes of hydrogen and oxygen are mixed. The ratio of speed of sound in the mixture to that in hydrogen is
1 \(\sqrt{\dfrac{1}{8}}\)
2 \(\sqrt{\dfrac{32}{17}}\)
3 \(\sqrt{8}\)
4 \(\sqrt{\dfrac{2}{17}}\)
Explanation:
Density of mixture \(\begin{aligned}& =\rho_{\text {mix }}=\dfrac{V_{o_{2}} \rho_{o_{2}}+V_{H_{2}} \rho_{H_{2}}}{V_{o_{2}}+V_{H_{2}}} \\& =\dfrac{V\left(\rho_{\mathrm{O}_{2}}+\rho_{H_{2}}\right)}{2 V}=\dfrac{\rho_{\mathrm{O}_{2}}+\rho_{H_{2}}}{2}\end{aligned}\) where \({V_{{O_2}}} = {V_{{H_2}}} = V\) \(=\dfrac{\rho_{H_{2}}+16 \rho_{H_{2}}}{2}=8.5 \rho_{H_{2}}\) The velocity is related with density as \(\begin{aligned}& v \alpha \dfrac{1}{\sqrt{\rho}} \\& \Rightarrow \dfrac{v_{\text {mix }}}{v_{H_{2}}}=\sqrt{\dfrac{\rho_{H_{2}}}{\rho_{\text {mix }}}}=\sqrt{\dfrac{\rho_{H_{2}}}{8.5 \rho_{H_{2}}}}=\sqrt{\dfrac{2}{17}}\end{aligned}\)
PHXI15:WAVES
354646
Assertion : Sound travels faster in solids than gases. Reason : Solid possesses greater density than gases.
1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
Explanation:
Sound travels faster in solids due to their higher density , which allows for quicker transmission of mechanical waves through closely packed particles. The reason is also true as it correctly attributes the faster sound propagation in solids to their greater density compared to gases. So option (1) is correct.
PHXI15:WAVES
354647
It takes of 2.0 seconds for a sound wave to travel between two fixed points when the day temperature is \(10^\circ C\). If the temperature rise to \(30^\circ C\) the sound wave travels between the same fixed parts in
1 \(2.0\,{\mkern 1mu} \sec \)
2 \(1.9{\mkern 1mu} \,\sec \)
3 \(2.2\,{\mkern 1mu} \sec \)
4 \(2.1{\mkern 1mu} \,\sec \)
Explanation:
Suppose the distance between two fixed points is \(d\) then \(t=\dfrac{d}{v}\) also \(v \propto \sqrt{T}=\dfrac{t_{1}}{t_{2}}=\dfrac{v_{2}}{v_{1}}=\sqrt{\dfrac{T_{2}}{T_{1}}}\) \(\Rightarrow \dfrac{2}{t_{2}}=\sqrt{\dfrac{303}{283}} \Rightarrow t_{2}=1.9 \mathrm{sec}\).
354643
Assertion : The fundamental frequency of an open organ pipe increases as the temperature is increased. Reason : As the temperature increases, the velocity of sound increases more rapidly than length of the pipe
1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Both Assertion and Reason are incorrect.
Explanation:
We know that the fundamental frequency of open organ pipe is given by \(f=\dfrac{v}{2 l}(v-\) velocity of sound). Hence as temperature increases \(v\) increases and therefore \(f\) increases. So assertion and reason are correct and reason supports assertion.
AIIMS - 2011
PHXI15:WAVES
354644
According to Laplace correction, the propagation of sound in gas takes place under
1 Isothermal condition
2 Isobaric condition
3 Isochoric condition
4 Adiabatic condition
Explanation:
Conceptual Question
PHXI15:WAVES
354645
Oxygen is 16 times heavier than hydrogen. Equal volumes of hydrogen and oxygen are mixed. The ratio of speed of sound in the mixture to that in hydrogen is
1 \(\sqrt{\dfrac{1}{8}}\)
2 \(\sqrt{\dfrac{32}{17}}\)
3 \(\sqrt{8}\)
4 \(\sqrt{\dfrac{2}{17}}\)
Explanation:
Density of mixture \(\begin{aligned}& =\rho_{\text {mix }}=\dfrac{V_{o_{2}} \rho_{o_{2}}+V_{H_{2}} \rho_{H_{2}}}{V_{o_{2}}+V_{H_{2}}} \\& =\dfrac{V\left(\rho_{\mathrm{O}_{2}}+\rho_{H_{2}}\right)}{2 V}=\dfrac{\rho_{\mathrm{O}_{2}}+\rho_{H_{2}}}{2}\end{aligned}\) where \({V_{{O_2}}} = {V_{{H_2}}} = V\) \(=\dfrac{\rho_{H_{2}}+16 \rho_{H_{2}}}{2}=8.5 \rho_{H_{2}}\) The velocity is related with density as \(\begin{aligned}& v \alpha \dfrac{1}{\sqrt{\rho}} \\& \Rightarrow \dfrac{v_{\text {mix }}}{v_{H_{2}}}=\sqrt{\dfrac{\rho_{H_{2}}}{\rho_{\text {mix }}}}=\sqrt{\dfrac{\rho_{H_{2}}}{8.5 \rho_{H_{2}}}}=\sqrt{\dfrac{2}{17}}\end{aligned}\)
PHXI15:WAVES
354646
Assertion : Sound travels faster in solids than gases. Reason : Solid possesses greater density than gases.
1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
Explanation:
Sound travels faster in solids due to their higher density , which allows for quicker transmission of mechanical waves through closely packed particles. The reason is also true as it correctly attributes the faster sound propagation in solids to their greater density compared to gases. So option (1) is correct.
PHXI15:WAVES
354647
It takes of 2.0 seconds for a sound wave to travel between two fixed points when the day temperature is \(10^\circ C\). If the temperature rise to \(30^\circ C\) the sound wave travels between the same fixed parts in
1 \(2.0\,{\mkern 1mu} \sec \)
2 \(1.9{\mkern 1mu} \,\sec \)
3 \(2.2\,{\mkern 1mu} \sec \)
4 \(2.1{\mkern 1mu} \,\sec \)
Explanation:
Suppose the distance between two fixed points is \(d\) then \(t=\dfrac{d}{v}\) also \(v \propto \sqrt{T}=\dfrac{t_{1}}{t_{2}}=\dfrac{v_{2}}{v_{1}}=\sqrt{\dfrac{T_{2}}{T_{1}}}\) \(\Rightarrow \dfrac{2}{t_{2}}=\sqrt{\dfrac{303}{283}} \Rightarrow t_{2}=1.9 \mathrm{sec}\).
354643
Assertion : The fundamental frequency of an open organ pipe increases as the temperature is increased. Reason : As the temperature increases, the velocity of sound increases more rapidly than length of the pipe
1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Both Assertion and Reason are incorrect.
Explanation:
We know that the fundamental frequency of open organ pipe is given by \(f=\dfrac{v}{2 l}(v-\) velocity of sound). Hence as temperature increases \(v\) increases and therefore \(f\) increases. So assertion and reason are correct and reason supports assertion.
AIIMS - 2011
PHXI15:WAVES
354644
According to Laplace correction, the propagation of sound in gas takes place under
1 Isothermal condition
2 Isobaric condition
3 Isochoric condition
4 Adiabatic condition
Explanation:
Conceptual Question
PHXI15:WAVES
354645
Oxygen is 16 times heavier than hydrogen. Equal volumes of hydrogen and oxygen are mixed. The ratio of speed of sound in the mixture to that in hydrogen is
1 \(\sqrt{\dfrac{1}{8}}\)
2 \(\sqrt{\dfrac{32}{17}}\)
3 \(\sqrt{8}\)
4 \(\sqrt{\dfrac{2}{17}}\)
Explanation:
Density of mixture \(\begin{aligned}& =\rho_{\text {mix }}=\dfrac{V_{o_{2}} \rho_{o_{2}}+V_{H_{2}} \rho_{H_{2}}}{V_{o_{2}}+V_{H_{2}}} \\& =\dfrac{V\left(\rho_{\mathrm{O}_{2}}+\rho_{H_{2}}\right)}{2 V}=\dfrac{\rho_{\mathrm{O}_{2}}+\rho_{H_{2}}}{2}\end{aligned}\) where \({V_{{O_2}}} = {V_{{H_2}}} = V\) \(=\dfrac{\rho_{H_{2}}+16 \rho_{H_{2}}}{2}=8.5 \rho_{H_{2}}\) The velocity is related with density as \(\begin{aligned}& v \alpha \dfrac{1}{\sqrt{\rho}} \\& \Rightarrow \dfrac{v_{\text {mix }}}{v_{H_{2}}}=\sqrt{\dfrac{\rho_{H_{2}}}{\rho_{\text {mix }}}}=\sqrt{\dfrac{\rho_{H_{2}}}{8.5 \rho_{H_{2}}}}=\sqrt{\dfrac{2}{17}}\end{aligned}\)
PHXI15:WAVES
354646
Assertion : Sound travels faster in solids than gases. Reason : Solid possesses greater density than gases.
1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
Explanation:
Sound travels faster in solids due to their higher density , which allows for quicker transmission of mechanical waves through closely packed particles. The reason is also true as it correctly attributes the faster sound propagation in solids to their greater density compared to gases. So option (1) is correct.
PHXI15:WAVES
354647
It takes of 2.0 seconds for a sound wave to travel between two fixed points when the day temperature is \(10^\circ C\). If the temperature rise to \(30^\circ C\) the sound wave travels between the same fixed parts in
1 \(2.0\,{\mkern 1mu} \sec \)
2 \(1.9{\mkern 1mu} \,\sec \)
3 \(2.2\,{\mkern 1mu} \sec \)
4 \(2.1{\mkern 1mu} \,\sec \)
Explanation:
Suppose the distance between two fixed points is \(d\) then \(t=\dfrac{d}{v}\) also \(v \propto \sqrt{T}=\dfrac{t_{1}}{t_{2}}=\dfrac{v_{2}}{v_{1}}=\sqrt{\dfrac{T_{2}}{T_{1}}}\) \(\Rightarrow \dfrac{2}{t_{2}}=\sqrt{\dfrac{303}{283}} \Rightarrow t_{2}=1.9 \mathrm{sec}\).
354643
Assertion : The fundamental frequency of an open organ pipe increases as the temperature is increased. Reason : As the temperature increases, the velocity of sound increases more rapidly than length of the pipe
1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Both Assertion and Reason are incorrect.
Explanation:
We know that the fundamental frequency of open organ pipe is given by \(f=\dfrac{v}{2 l}(v-\) velocity of sound). Hence as temperature increases \(v\) increases and therefore \(f\) increases. So assertion and reason are correct and reason supports assertion.
AIIMS - 2011
PHXI15:WAVES
354644
According to Laplace correction, the propagation of sound in gas takes place under
1 Isothermal condition
2 Isobaric condition
3 Isochoric condition
4 Adiabatic condition
Explanation:
Conceptual Question
PHXI15:WAVES
354645
Oxygen is 16 times heavier than hydrogen. Equal volumes of hydrogen and oxygen are mixed. The ratio of speed of sound in the mixture to that in hydrogen is
1 \(\sqrt{\dfrac{1}{8}}\)
2 \(\sqrt{\dfrac{32}{17}}\)
3 \(\sqrt{8}\)
4 \(\sqrt{\dfrac{2}{17}}\)
Explanation:
Density of mixture \(\begin{aligned}& =\rho_{\text {mix }}=\dfrac{V_{o_{2}} \rho_{o_{2}}+V_{H_{2}} \rho_{H_{2}}}{V_{o_{2}}+V_{H_{2}}} \\& =\dfrac{V\left(\rho_{\mathrm{O}_{2}}+\rho_{H_{2}}\right)}{2 V}=\dfrac{\rho_{\mathrm{O}_{2}}+\rho_{H_{2}}}{2}\end{aligned}\) where \({V_{{O_2}}} = {V_{{H_2}}} = V\) \(=\dfrac{\rho_{H_{2}}+16 \rho_{H_{2}}}{2}=8.5 \rho_{H_{2}}\) The velocity is related with density as \(\begin{aligned}& v \alpha \dfrac{1}{\sqrt{\rho}} \\& \Rightarrow \dfrac{v_{\text {mix }}}{v_{H_{2}}}=\sqrt{\dfrac{\rho_{H_{2}}}{\rho_{\text {mix }}}}=\sqrt{\dfrac{\rho_{H_{2}}}{8.5 \rho_{H_{2}}}}=\sqrt{\dfrac{2}{17}}\end{aligned}\)
PHXI15:WAVES
354646
Assertion : Sound travels faster in solids than gases. Reason : Solid possesses greater density than gases.
1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
Explanation:
Sound travels faster in solids due to their higher density , which allows for quicker transmission of mechanical waves through closely packed particles. The reason is also true as it correctly attributes the faster sound propagation in solids to their greater density compared to gases. So option (1) is correct.
PHXI15:WAVES
354647
It takes of 2.0 seconds for a sound wave to travel between two fixed points when the day temperature is \(10^\circ C\). If the temperature rise to \(30^\circ C\) the sound wave travels between the same fixed parts in
1 \(2.0\,{\mkern 1mu} \sec \)
2 \(1.9{\mkern 1mu} \,\sec \)
3 \(2.2\,{\mkern 1mu} \sec \)
4 \(2.1{\mkern 1mu} \,\sec \)
Explanation:
Suppose the distance between two fixed points is \(d\) then \(t=\dfrac{d}{v}\) also \(v \propto \sqrt{T}=\dfrac{t_{1}}{t_{2}}=\dfrac{v_{2}}{v_{1}}=\sqrt{\dfrac{T_{2}}{T_{1}}}\) \(\Rightarrow \dfrac{2}{t_{2}}=\sqrt{\dfrac{303}{283}} \Rightarrow t_{2}=1.9 \mathrm{sec}\).
