354656
\(v_{1}\) and \(v_{2}\) are the velocities of sound at the same temperature in two monoatomic gases of densities \(\rho_{1}\) and \(\rho_{2}\) respectively. If \(\rho_{1} / \rho_{2}=\dfrac{1}{4}\) then the ratio of velocities \(v_{1}\) and \(v_{2}\) will be
1 \(4: 1\)
2 \(1: 2\)
3 \(1: 4\)
4 \(2: 1\)
Explanation:
At given temperature and pressure \(v \propto \dfrac{1}{\sqrt{\rho}} \Rightarrow \dfrac{v_{1}}{v_{2}}=\sqrt{\dfrac{\rho_{2}}{\rho_{1}}}=\sqrt{\dfrac{4}{1}}=2: 1 .\)
PHXI15:WAVES
354657
A stone dropped from the top of a tower of height \(300\;m\) high splashes into the water of a pond near the base of the tower. When is the splash heard at the top given that the speed of sound in air is \(340\;m/s?\left( {g = 9.8\;m/{s^2}} \right)\)
1 \(9.7\;s\)
2 \(8.7\;s\)
3 \(6.7\;s\)
4 \(10\;s\)
Explanation:
Height of tower \((h)=300 m\) Initial velocity \(u=0\) Acceleration due to gravity \(g = 9.8\;m/{s^2}\) Speed of sound in air \( = 340\;m/s\) Time taken by stone to reach the pond \(=t_{1}\) Using equation of motion, \(h = ut + \frac{1}{2}gt_1^2 \Rightarrow 300 = 0 + \frac{1}{2} \times 9.8t_1^2\) \( \Rightarrow {t_1} = \sqrt {\frac{{300 \times 2}}{{9.8}}} = 7.82\;s\) Time taken by the sound to reach the top of the tower \({t_2} = \frac{h}{v} = \frac{{300}}{{340}} = 0.88\;s\) \(\therefore \;\;\;{\mkern 1mu} {\text{Total}}\,{\text{time }}t = {t_1} + {t_2} = 7.82 + 0.88 = 8.7\;s\)
NCERT Exemplar
PHXI15:WAVES
354658
Assertion : The basic of Laplace correction was that exchange of heat between the region of compression and rarefaction in air is not possible if it is isothermal. Reason : Air is a bad conductor of heat and velocity of sound in air is appreciably large.
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:
According to Laplace, when sound waves propagate through a gas, the associated changes in pressure and volume do not occur isothermally but rather follow an adiabatic process. So in these pressure waves (Sound), there will be modifications in temperature with heat to layers. So correct option is (1).
PHXI15:WAVES
354659
Speed of sound at constant temperature depends on
1 Density of gas
2 Pressure
3 Both (1) and (2)
4 None of these
Explanation:
Speed of sound, doesn't depend upon pressure and density of the medium at constant temperature.
PHXI15:WAVES
354660
Assertion : Sound would travel faster on a hot summer day than on a cold winter day. Reason : Velocity of sound is directly proportional to the square of its absolute temperature.
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:
The velocity of sound in a gas is directly proportional to the square root of its absolute temperature \(\left(\right.\) as \(\left.v=\sqrt{\dfrac{\gamma R T}{M}}\right)\). Since temperature of a hot day is more than cold winter day, therefore sound would travel faster on a hot summer day than on a cold winter day.
354656
\(v_{1}\) and \(v_{2}\) are the velocities of sound at the same temperature in two monoatomic gases of densities \(\rho_{1}\) and \(\rho_{2}\) respectively. If \(\rho_{1} / \rho_{2}=\dfrac{1}{4}\) then the ratio of velocities \(v_{1}\) and \(v_{2}\) will be
1 \(4: 1\)
2 \(1: 2\)
3 \(1: 4\)
4 \(2: 1\)
Explanation:
At given temperature and pressure \(v \propto \dfrac{1}{\sqrt{\rho}} \Rightarrow \dfrac{v_{1}}{v_{2}}=\sqrt{\dfrac{\rho_{2}}{\rho_{1}}}=\sqrt{\dfrac{4}{1}}=2: 1 .\)
PHXI15:WAVES
354657
A stone dropped from the top of a tower of height \(300\;m\) high splashes into the water of a pond near the base of the tower. When is the splash heard at the top given that the speed of sound in air is \(340\;m/s?\left( {g = 9.8\;m/{s^2}} \right)\)
1 \(9.7\;s\)
2 \(8.7\;s\)
3 \(6.7\;s\)
4 \(10\;s\)
Explanation:
Height of tower \((h)=300 m\) Initial velocity \(u=0\) Acceleration due to gravity \(g = 9.8\;m/{s^2}\) Speed of sound in air \( = 340\;m/s\) Time taken by stone to reach the pond \(=t_{1}\) Using equation of motion, \(h = ut + \frac{1}{2}gt_1^2 \Rightarrow 300 = 0 + \frac{1}{2} \times 9.8t_1^2\) \( \Rightarrow {t_1} = \sqrt {\frac{{300 \times 2}}{{9.8}}} = 7.82\;s\) Time taken by the sound to reach the top of the tower \({t_2} = \frac{h}{v} = \frac{{300}}{{340}} = 0.88\;s\) \(\therefore \;\;\;{\mkern 1mu} {\text{Total}}\,{\text{time }}t = {t_1} + {t_2} = 7.82 + 0.88 = 8.7\;s\)
NCERT Exemplar
PHXI15:WAVES
354658
Assertion : The basic of Laplace correction was that exchange of heat between the region of compression and rarefaction in air is not possible if it is isothermal. Reason : Air is a bad conductor of heat and velocity of sound in air is appreciably large.
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:
According to Laplace, when sound waves propagate through a gas, the associated changes in pressure and volume do not occur isothermally but rather follow an adiabatic process. So in these pressure waves (Sound), there will be modifications in temperature with heat to layers. So correct option is (1).
PHXI15:WAVES
354659
Speed of sound at constant temperature depends on
1 Density of gas
2 Pressure
3 Both (1) and (2)
4 None of these
Explanation:
Speed of sound, doesn't depend upon pressure and density of the medium at constant temperature.
PHXI15:WAVES
354660
Assertion : Sound would travel faster on a hot summer day than on a cold winter day. Reason : Velocity of sound is directly proportional to the square of its absolute temperature.
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:
The velocity of sound in a gas is directly proportional to the square root of its absolute temperature \(\left(\right.\) as \(\left.v=\sqrt{\dfrac{\gamma R T}{M}}\right)\). Since temperature of a hot day is more than cold winter day, therefore sound would travel faster on a hot summer day than on a cold winter day.
354656
\(v_{1}\) and \(v_{2}\) are the velocities of sound at the same temperature in two monoatomic gases of densities \(\rho_{1}\) and \(\rho_{2}\) respectively. If \(\rho_{1} / \rho_{2}=\dfrac{1}{4}\) then the ratio of velocities \(v_{1}\) and \(v_{2}\) will be
1 \(4: 1\)
2 \(1: 2\)
3 \(1: 4\)
4 \(2: 1\)
Explanation:
At given temperature and pressure \(v \propto \dfrac{1}{\sqrt{\rho}} \Rightarrow \dfrac{v_{1}}{v_{2}}=\sqrt{\dfrac{\rho_{2}}{\rho_{1}}}=\sqrt{\dfrac{4}{1}}=2: 1 .\)
PHXI15:WAVES
354657
A stone dropped from the top of a tower of height \(300\;m\) high splashes into the water of a pond near the base of the tower. When is the splash heard at the top given that the speed of sound in air is \(340\;m/s?\left( {g = 9.8\;m/{s^2}} \right)\)
1 \(9.7\;s\)
2 \(8.7\;s\)
3 \(6.7\;s\)
4 \(10\;s\)
Explanation:
Height of tower \((h)=300 m\) Initial velocity \(u=0\) Acceleration due to gravity \(g = 9.8\;m/{s^2}\) Speed of sound in air \( = 340\;m/s\) Time taken by stone to reach the pond \(=t_{1}\) Using equation of motion, \(h = ut + \frac{1}{2}gt_1^2 \Rightarrow 300 = 0 + \frac{1}{2} \times 9.8t_1^2\) \( \Rightarrow {t_1} = \sqrt {\frac{{300 \times 2}}{{9.8}}} = 7.82\;s\) Time taken by the sound to reach the top of the tower \({t_2} = \frac{h}{v} = \frac{{300}}{{340}} = 0.88\;s\) \(\therefore \;\;\;{\mkern 1mu} {\text{Total}}\,{\text{time }}t = {t_1} + {t_2} = 7.82 + 0.88 = 8.7\;s\)
NCERT Exemplar
PHXI15:WAVES
354658
Assertion : The basic of Laplace correction was that exchange of heat between the region of compression and rarefaction in air is not possible if it is isothermal. Reason : Air is a bad conductor of heat and velocity of sound in air is appreciably large.
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:
According to Laplace, when sound waves propagate through a gas, the associated changes in pressure and volume do not occur isothermally but rather follow an adiabatic process. So in these pressure waves (Sound), there will be modifications in temperature with heat to layers. So correct option is (1).
PHXI15:WAVES
354659
Speed of sound at constant temperature depends on
1 Density of gas
2 Pressure
3 Both (1) and (2)
4 None of these
Explanation:
Speed of sound, doesn't depend upon pressure and density of the medium at constant temperature.
PHXI15:WAVES
354660
Assertion : Sound would travel faster on a hot summer day than on a cold winter day. Reason : Velocity of sound is directly proportional to the square of its absolute temperature.
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:
The velocity of sound in a gas is directly proportional to the square root of its absolute temperature \(\left(\right.\) as \(\left.v=\sqrt{\dfrac{\gamma R T}{M}}\right)\). Since temperature of a hot day is more than cold winter day, therefore sound would travel faster on a hot summer day than on a cold winter day.
354656
\(v_{1}\) and \(v_{2}\) are the velocities of sound at the same temperature in two monoatomic gases of densities \(\rho_{1}\) and \(\rho_{2}\) respectively. If \(\rho_{1} / \rho_{2}=\dfrac{1}{4}\) then the ratio of velocities \(v_{1}\) and \(v_{2}\) will be
1 \(4: 1\)
2 \(1: 2\)
3 \(1: 4\)
4 \(2: 1\)
Explanation:
At given temperature and pressure \(v \propto \dfrac{1}{\sqrt{\rho}} \Rightarrow \dfrac{v_{1}}{v_{2}}=\sqrt{\dfrac{\rho_{2}}{\rho_{1}}}=\sqrt{\dfrac{4}{1}}=2: 1 .\)
PHXI15:WAVES
354657
A stone dropped from the top of a tower of height \(300\;m\) high splashes into the water of a pond near the base of the tower. When is the splash heard at the top given that the speed of sound in air is \(340\;m/s?\left( {g = 9.8\;m/{s^2}} \right)\)
1 \(9.7\;s\)
2 \(8.7\;s\)
3 \(6.7\;s\)
4 \(10\;s\)
Explanation:
Height of tower \((h)=300 m\) Initial velocity \(u=0\) Acceleration due to gravity \(g = 9.8\;m/{s^2}\) Speed of sound in air \( = 340\;m/s\) Time taken by stone to reach the pond \(=t_{1}\) Using equation of motion, \(h = ut + \frac{1}{2}gt_1^2 \Rightarrow 300 = 0 + \frac{1}{2} \times 9.8t_1^2\) \( \Rightarrow {t_1} = \sqrt {\frac{{300 \times 2}}{{9.8}}} = 7.82\;s\) Time taken by the sound to reach the top of the tower \({t_2} = \frac{h}{v} = \frac{{300}}{{340}} = 0.88\;s\) \(\therefore \;\;\;{\mkern 1mu} {\text{Total}}\,{\text{time }}t = {t_1} + {t_2} = 7.82 + 0.88 = 8.7\;s\)
NCERT Exemplar
PHXI15:WAVES
354658
Assertion : The basic of Laplace correction was that exchange of heat between the region of compression and rarefaction in air is not possible if it is isothermal. Reason : Air is a bad conductor of heat and velocity of sound in air is appreciably large.
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:
According to Laplace, when sound waves propagate through a gas, the associated changes in pressure and volume do not occur isothermally but rather follow an adiabatic process. So in these pressure waves (Sound), there will be modifications in temperature with heat to layers. So correct option is (1).
PHXI15:WAVES
354659
Speed of sound at constant temperature depends on
1 Density of gas
2 Pressure
3 Both (1) and (2)
4 None of these
Explanation:
Speed of sound, doesn't depend upon pressure and density of the medium at constant temperature.
PHXI15:WAVES
354660
Assertion : Sound would travel faster on a hot summer day than on a cold winter day. Reason : Velocity of sound is directly proportional to the square of its absolute temperature.
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:
The velocity of sound in a gas is directly proportional to the square root of its absolute temperature \(\left(\right.\) as \(\left.v=\sqrt{\dfrac{\gamma R T}{M}}\right)\). Since temperature of a hot day is more than cold winter day, therefore sound would travel faster on a hot summer day than on a cold winter day.
354656
\(v_{1}\) and \(v_{2}\) are the velocities of sound at the same temperature in two monoatomic gases of densities \(\rho_{1}\) and \(\rho_{2}\) respectively. If \(\rho_{1} / \rho_{2}=\dfrac{1}{4}\) then the ratio of velocities \(v_{1}\) and \(v_{2}\) will be
1 \(4: 1\)
2 \(1: 2\)
3 \(1: 4\)
4 \(2: 1\)
Explanation:
At given temperature and pressure \(v \propto \dfrac{1}{\sqrt{\rho}} \Rightarrow \dfrac{v_{1}}{v_{2}}=\sqrt{\dfrac{\rho_{2}}{\rho_{1}}}=\sqrt{\dfrac{4}{1}}=2: 1 .\)
PHXI15:WAVES
354657
A stone dropped from the top of a tower of height \(300\;m\) high splashes into the water of a pond near the base of the tower. When is the splash heard at the top given that the speed of sound in air is \(340\;m/s?\left( {g = 9.8\;m/{s^2}} \right)\)
1 \(9.7\;s\)
2 \(8.7\;s\)
3 \(6.7\;s\)
4 \(10\;s\)
Explanation:
Height of tower \((h)=300 m\) Initial velocity \(u=0\) Acceleration due to gravity \(g = 9.8\;m/{s^2}\) Speed of sound in air \( = 340\;m/s\) Time taken by stone to reach the pond \(=t_{1}\) Using equation of motion, \(h = ut + \frac{1}{2}gt_1^2 \Rightarrow 300 = 0 + \frac{1}{2} \times 9.8t_1^2\) \( \Rightarrow {t_1} = \sqrt {\frac{{300 \times 2}}{{9.8}}} = 7.82\;s\) Time taken by the sound to reach the top of the tower \({t_2} = \frac{h}{v} = \frac{{300}}{{340}} = 0.88\;s\) \(\therefore \;\;\;{\mkern 1mu} {\text{Total}}\,{\text{time }}t = {t_1} + {t_2} = 7.82 + 0.88 = 8.7\;s\)
NCERT Exemplar
PHXI15:WAVES
354658
Assertion : The basic of Laplace correction was that exchange of heat between the region of compression and rarefaction in air is not possible if it is isothermal. Reason : Air is a bad conductor of heat and velocity of sound in air is appreciably large.
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:
According to Laplace, when sound waves propagate through a gas, the associated changes in pressure and volume do not occur isothermally but rather follow an adiabatic process. So in these pressure waves (Sound), there will be modifications in temperature with heat to layers. So correct option is (1).
PHXI15:WAVES
354659
Speed of sound at constant temperature depends on
1 Density of gas
2 Pressure
3 Both (1) and (2)
4 None of these
Explanation:
Speed of sound, doesn't depend upon pressure and density of the medium at constant temperature.
PHXI15:WAVES
354660
Assertion : Sound would travel faster on a hot summer day than on a cold winter day. Reason : Velocity of sound is directly proportional to the square of its absolute temperature.
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:
The velocity of sound in a gas is directly proportional to the square root of its absolute temperature \(\left(\right.\) as \(\left.v=\sqrt{\dfrac{\gamma R T}{M}}\right)\). Since temperature of a hot day is more than cold winter day, therefore sound would travel faster on a hot summer day than on a cold winter day.
