354673
Assertion : The velocity of sound in hydrogen gas is less than the velocity of sound in oxygen gas. Reason : The density of hydrogen is more than the density of oxygen.
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 gaseous medium is determined by the equation \(v=\sqrt{\dfrac{\gamma P}{\rho}}\). It is evident that the speed of sound in a gas is inversely proportional to the square root of the gas's density. Given that the density of oxygen is 16 times greater than that of hydrogen, it follows that the velocity of sound in hydrogen is four times greater than the velocity of sound in oxygen. So correct option is (4).
PHXI15:WAVES
354674
Find the ratio of velocities of sound in Helium and hydrogen gases at \(27^\circ C\).
354675
The ratio of the speed of sound in nitrogen gas to that in helium gas, at \(400\;K\) is
1 \(\sqrt{\dfrac{3}{7}}\)
2 \(\sqrt{\dfrac{3}{4}}\)
3 \(\sqrt{\dfrac{3}{5}}\)
4 \(\sqrt{\dfrac{3}{25}}\)
Explanation:
\(v=\sqrt{\dfrac{\gamma R T}{M}}\) \(\begin{aligned}& \dfrac{v_{1}}{v_{2}}=\sqrt{\dfrac{\gamma_{1} M_{2}}{\gamma_{2} M_{1}}} \\& M_{1}=28 g m, M_{2}=4 g m \\& \gamma_{1}=\dfrac{7}{5}, \gamma_{2}=\dfrac{5}{3} \\& \dfrac{v_{1}}{v_{2}}=\sqrt{\dfrac{7}{5} \times \dfrac{3}{5} \times \dfrac{4}{28}}=\sqrt{\dfrac{3}{25}}\end{aligned}\)
PHXI15:WAVES
354676
The speed of sound in oxygen at S.T.P. will be approximately (given, \({R=8.3 {JK}^{-1}, \gamma=1.4}\) )
1 \({341 {~m} / {s}}\)
2 \({310 {~m} / {s}}\)
3 \({325 {~m} / {s}}\)
4 \({333 {~m} / {s}}\)
Explanation:
\({v=\sqrt{\dfrac{\gamma P}{\rho}}}\) As, Density of oxygen at STP \({\rho=\dfrac{\text { Mass }}{\text { Volume }}=\dfrac{32 \times 10^{-3}}{22.4 \times 10^{-3}}}\) \({\Rightarrow \rho=1.4286 {~kg} {~m}^{-3}}\) Pressure, \({P=1.013 \times 10^{5} {~Pa}}\) Speed of sound, \({v=\sqrt{\dfrac{1.4 \times 1.013 \times 10^{5}}{1.4286}}}\) \({v=315 m / s}\) Option (2) is more suitable answer..
JEE - 2024
PHXI15:WAVES
354677
Sound waves travel at \(350\;m/s\) through a warm air and at \(3500\;m/s\) through brass. The wavelength of a \(700\,Hz\) acoustic wave as it enters brass from warm air
354673
Assertion : The velocity of sound in hydrogen gas is less than the velocity of sound in oxygen gas. Reason : The density of hydrogen is more than the density of oxygen.
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 gaseous medium is determined by the equation \(v=\sqrt{\dfrac{\gamma P}{\rho}}\). It is evident that the speed of sound in a gas is inversely proportional to the square root of the gas's density. Given that the density of oxygen is 16 times greater than that of hydrogen, it follows that the velocity of sound in hydrogen is four times greater than the velocity of sound in oxygen. So correct option is (4).
PHXI15:WAVES
354674
Find the ratio of velocities of sound in Helium and hydrogen gases at \(27^\circ C\).
354675
The ratio of the speed of sound in nitrogen gas to that in helium gas, at \(400\;K\) is
1 \(\sqrt{\dfrac{3}{7}}\)
2 \(\sqrt{\dfrac{3}{4}}\)
3 \(\sqrt{\dfrac{3}{5}}\)
4 \(\sqrt{\dfrac{3}{25}}\)
Explanation:
\(v=\sqrt{\dfrac{\gamma R T}{M}}\) \(\begin{aligned}& \dfrac{v_{1}}{v_{2}}=\sqrt{\dfrac{\gamma_{1} M_{2}}{\gamma_{2} M_{1}}} \\& M_{1}=28 g m, M_{2}=4 g m \\& \gamma_{1}=\dfrac{7}{5}, \gamma_{2}=\dfrac{5}{3} \\& \dfrac{v_{1}}{v_{2}}=\sqrt{\dfrac{7}{5} \times \dfrac{3}{5} \times \dfrac{4}{28}}=\sqrt{\dfrac{3}{25}}\end{aligned}\)
PHXI15:WAVES
354676
The speed of sound in oxygen at S.T.P. will be approximately (given, \({R=8.3 {JK}^{-1}, \gamma=1.4}\) )
1 \({341 {~m} / {s}}\)
2 \({310 {~m} / {s}}\)
3 \({325 {~m} / {s}}\)
4 \({333 {~m} / {s}}\)
Explanation:
\({v=\sqrt{\dfrac{\gamma P}{\rho}}}\) As, Density of oxygen at STP \({\rho=\dfrac{\text { Mass }}{\text { Volume }}=\dfrac{32 \times 10^{-3}}{22.4 \times 10^{-3}}}\) \({\Rightarrow \rho=1.4286 {~kg} {~m}^{-3}}\) Pressure, \({P=1.013 \times 10^{5} {~Pa}}\) Speed of sound, \({v=\sqrt{\dfrac{1.4 \times 1.013 \times 10^{5}}{1.4286}}}\) \({v=315 m / s}\) Option (2) is more suitable answer..
JEE - 2024
PHXI15:WAVES
354677
Sound waves travel at \(350\;m/s\) through a warm air and at \(3500\;m/s\) through brass. The wavelength of a \(700\,Hz\) acoustic wave as it enters brass from warm air
354673
Assertion : The velocity of sound in hydrogen gas is less than the velocity of sound in oxygen gas. Reason : The density of hydrogen is more than the density of oxygen.
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 gaseous medium is determined by the equation \(v=\sqrt{\dfrac{\gamma P}{\rho}}\). It is evident that the speed of sound in a gas is inversely proportional to the square root of the gas's density. Given that the density of oxygen is 16 times greater than that of hydrogen, it follows that the velocity of sound in hydrogen is four times greater than the velocity of sound in oxygen. So correct option is (4).
PHXI15:WAVES
354674
Find the ratio of velocities of sound in Helium and hydrogen gases at \(27^\circ C\).
354675
The ratio of the speed of sound in nitrogen gas to that in helium gas, at \(400\;K\) is
1 \(\sqrt{\dfrac{3}{7}}\)
2 \(\sqrt{\dfrac{3}{4}}\)
3 \(\sqrt{\dfrac{3}{5}}\)
4 \(\sqrt{\dfrac{3}{25}}\)
Explanation:
\(v=\sqrt{\dfrac{\gamma R T}{M}}\) \(\begin{aligned}& \dfrac{v_{1}}{v_{2}}=\sqrt{\dfrac{\gamma_{1} M_{2}}{\gamma_{2} M_{1}}} \\& M_{1}=28 g m, M_{2}=4 g m \\& \gamma_{1}=\dfrac{7}{5}, \gamma_{2}=\dfrac{5}{3} \\& \dfrac{v_{1}}{v_{2}}=\sqrt{\dfrac{7}{5} \times \dfrac{3}{5} \times \dfrac{4}{28}}=\sqrt{\dfrac{3}{25}}\end{aligned}\)
PHXI15:WAVES
354676
The speed of sound in oxygen at S.T.P. will be approximately (given, \({R=8.3 {JK}^{-1}, \gamma=1.4}\) )
1 \({341 {~m} / {s}}\)
2 \({310 {~m} / {s}}\)
3 \({325 {~m} / {s}}\)
4 \({333 {~m} / {s}}\)
Explanation:
\({v=\sqrt{\dfrac{\gamma P}{\rho}}}\) As, Density of oxygen at STP \({\rho=\dfrac{\text { Mass }}{\text { Volume }}=\dfrac{32 \times 10^{-3}}{22.4 \times 10^{-3}}}\) \({\Rightarrow \rho=1.4286 {~kg} {~m}^{-3}}\) Pressure, \({P=1.013 \times 10^{5} {~Pa}}\) Speed of sound, \({v=\sqrt{\dfrac{1.4 \times 1.013 \times 10^{5}}{1.4286}}}\) \({v=315 m / s}\) Option (2) is more suitable answer..
JEE - 2024
PHXI15:WAVES
354677
Sound waves travel at \(350\;m/s\) through a warm air and at \(3500\;m/s\) through brass. The wavelength of a \(700\,Hz\) acoustic wave as it enters brass from warm air
354673
Assertion : The velocity of sound in hydrogen gas is less than the velocity of sound in oxygen gas. Reason : The density of hydrogen is more than the density of oxygen.
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 gaseous medium is determined by the equation \(v=\sqrt{\dfrac{\gamma P}{\rho}}\). It is evident that the speed of sound in a gas is inversely proportional to the square root of the gas's density. Given that the density of oxygen is 16 times greater than that of hydrogen, it follows that the velocity of sound in hydrogen is four times greater than the velocity of sound in oxygen. So correct option is (4).
PHXI15:WAVES
354674
Find the ratio of velocities of sound in Helium and hydrogen gases at \(27^\circ C\).
354675
The ratio of the speed of sound in nitrogen gas to that in helium gas, at \(400\;K\) is
1 \(\sqrt{\dfrac{3}{7}}\)
2 \(\sqrt{\dfrac{3}{4}}\)
3 \(\sqrt{\dfrac{3}{5}}\)
4 \(\sqrt{\dfrac{3}{25}}\)
Explanation:
\(v=\sqrt{\dfrac{\gamma R T}{M}}\) \(\begin{aligned}& \dfrac{v_{1}}{v_{2}}=\sqrt{\dfrac{\gamma_{1} M_{2}}{\gamma_{2} M_{1}}} \\& M_{1}=28 g m, M_{2}=4 g m \\& \gamma_{1}=\dfrac{7}{5}, \gamma_{2}=\dfrac{5}{3} \\& \dfrac{v_{1}}{v_{2}}=\sqrt{\dfrac{7}{5} \times \dfrac{3}{5} \times \dfrac{4}{28}}=\sqrt{\dfrac{3}{25}}\end{aligned}\)
PHXI15:WAVES
354676
The speed of sound in oxygen at S.T.P. will be approximately (given, \({R=8.3 {JK}^{-1}, \gamma=1.4}\) )
1 \({341 {~m} / {s}}\)
2 \({310 {~m} / {s}}\)
3 \({325 {~m} / {s}}\)
4 \({333 {~m} / {s}}\)
Explanation:
\({v=\sqrt{\dfrac{\gamma P}{\rho}}}\) As, Density of oxygen at STP \({\rho=\dfrac{\text { Mass }}{\text { Volume }}=\dfrac{32 \times 10^{-3}}{22.4 \times 10^{-3}}}\) \({\Rightarrow \rho=1.4286 {~kg} {~m}^{-3}}\) Pressure, \({P=1.013 \times 10^{5} {~Pa}}\) Speed of sound, \({v=\sqrt{\dfrac{1.4 \times 1.013 \times 10^{5}}{1.4286}}}\) \({v=315 m / s}\) Option (2) is more suitable answer..
JEE - 2024
PHXI15:WAVES
354677
Sound waves travel at \(350\;m/s\) through a warm air and at \(3500\;m/s\) through brass. The wavelength of a \(700\,Hz\) acoustic wave as it enters brass from warm air
354673
Assertion : The velocity of sound in hydrogen gas is less than the velocity of sound in oxygen gas. Reason : The density of hydrogen is more than the density of oxygen.
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 gaseous medium is determined by the equation \(v=\sqrt{\dfrac{\gamma P}{\rho}}\). It is evident that the speed of sound in a gas is inversely proportional to the square root of the gas's density. Given that the density of oxygen is 16 times greater than that of hydrogen, it follows that the velocity of sound in hydrogen is four times greater than the velocity of sound in oxygen. So correct option is (4).
PHXI15:WAVES
354674
Find the ratio of velocities of sound in Helium and hydrogen gases at \(27^\circ C\).
354675
The ratio of the speed of sound in nitrogen gas to that in helium gas, at \(400\;K\) is
1 \(\sqrt{\dfrac{3}{7}}\)
2 \(\sqrt{\dfrac{3}{4}}\)
3 \(\sqrt{\dfrac{3}{5}}\)
4 \(\sqrt{\dfrac{3}{25}}\)
Explanation:
\(v=\sqrt{\dfrac{\gamma R T}{M}}\) \(\begin{aligned}& \dfrac{v_{1}}{v_{2}}=\sqrt{\dfrac{\gamma_{1} M_{2}}{\gamma_{2} M_{1}}} \\& M_{1}=28 g m, M_{2}=4 g m \\& \gamma_{1}=\dfrac{7}{5}, \gamma_{2}=\dfrac{5}{3} \\& \dfrac{v_{1}}{v_{2}}=\sqrt{\dfrac{7}{5} \times \dfrac{3}{5} \times \dfrac{4}{28}}=\sqrt{\dfrac{3}{25}}\end{aligned}\)
PHXI15:WAVES
354676
The speed of sound in oxygen at S.T.P. will be approximately (given, \({R=8.3 {JK}^{-1}, \gamma=1.4}\) )
1 \({341 {~m} / {s}}\)
2 \({310 {~m} / {s}}\)
3 \({325 {~m} / {s}}\)
4 \({333 {~m} / {s}}\)
Explanation:
\({v=\sqrt{\dfrac{\gamma P}{\rho}}}\) As, Density of oxygen at STP \({\rho=\dfrac{\text { Mass }}{\text { Volume }}=\dfrac{32 \times 10^{-3}}{22.4 \times 10^{-3}}}\) \({\Rightarrow \rho=1.4286 {~kg} {~m}^{-3}}\) Pressure, \({P=1.013 \times 10^{5} {~Pa}}\) Speed of sound, \({v=\sqrt{\dfrac{1.4 \times 1.013 \times 10^{5}}{1.4286}}}\) \({v=315 m / s}\) Option (2) is more suitable answer..
JEE - 2024
PHXI15:WAVES
354677
Sound waves travel at \(350\;m/s\) through a warm air and at \(3500\;m/s\) through brass. The wavelength of a \(700\,Hz\) acoustic wave as it enters brass from warm air
