354682
The ratio of the velocity of sound in hydrogen \((\gamma=7 / 5)\) to that in helium \((\gamma=5 / 3)\) at the same temperature is
1 \(\sqrt{\dfrac{5}{42}}\)
2 \(\sqrt{\dfrac{5}{21}}\)
3 \(\dfrac{\sqrt{42}}{5}\)
4 \(\dfrac{\sqrt{21}}{5}\)
Explanation:
Speed of sound in gas \(v=\sqrt{\dfrac{\gamma \mathrm{RT}}{\mathrm{M}}}\) Since the temperature is same for both the gases, \(\begin{aligned}& \dfrac{v_{H e}}{v_{H_{2}}}=\sqrt{\dfrac{\gamma_{H e} M_{H_{2}}}{\gamma_{H_{2}} M_{H e}}}=\sqrt{\dfrac{5 \times 5 \times 2}{3 \times 7 \times 4}}=\sqrt{\dfrac{25}{42}} \\& \Rightarrow \dfrac{v_{H_{2}}}{v_{H e}}=\dfrac{\sqrt{42}}{5}\end{aligned}\)
KCET - 2007
PHXI15:WAVES
354683
Sound velocity is maximum in
1 \({N_2}\)
2 \({H_2}\)
3 \({O_2}\)
4 \(He\)
Explanation:
\(v \propto \sqrt{\dfrac{\gamma}{M}}\) Since \(\dfrac{\gamma}{M}\) is maximum for \(H_{2}\) so sound velocity is maximum in \({H_2}.\)
PHXI15:WAVES
354684
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
354682
The ratio of the velocity of sound in hydrogen \((\gamma=7 / 5)\) to that in helium \((\gamma=5 / 3)\) at the same temperature is
1 \(\sqrt{\dfrac{5}{42}}\)
2 \(\sqrt{\dfrac{5}{21}}\)
3 \(\dfrac{\sqrt{42}}{5}\)
4 \(\dfrac{\sqrt{21}}{5}\)
Explanation:
Speed of sound in gas \(v=\sqrt{\dfrac{\gamma \mathrm{RT}}{\mathrm{M}}}\) Since the temperature is same for both the gases, \(\begin{aligned}& \dfrac{v_{H e}}{v_{H_{2}}}=\sqrt{\dfrac{\gamma_{H e} M_{H_{2}}}{\gamma_{H_{2}} M_{H e}}}=\sqrt{\dfrac{5 \times 5 \times 2}{3 \times 7 \times 4}}=\sqrt{\dfrac{25}{42}} \\& \Rightarrow \dfrac{v_{H_{2}}}{v_{H e}}=\dfrac{\sqrt{42}}{5}\end{aligned}\)
KCET - 2007
PHXI15:WAVES
354683
Sound velocity is maximum in
1 \({N_2}\)
2 \({H_2}\)
3 \({O_2}\)
4 \(He\)
Explanation:
\(v \propto \sqrt{\dfrac{\gamma}{M}}\) Since \(\dfrac{\gamma}{M}\) is maximum for \(H_{2}\) so sound velocity is maximum in \({H_2}.\)
PHXI15:WAVES
354684
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
354682
The ratio of the velocity of sound in hydrogen \((\gamma=7 / 5)\) to that in helium \((\gamma=5 / 3)\) at the same temperature is
1 \(\sqrt{\dfrac{5}{42}}\)
2 \(\sqrt{\dfrac{5}{21}}\)
3 \(\dfrac{\sqrt{42}}{5}\)
4 \(\dfrac{\sqrt{21}}{5}\)
Explanation:
Speed of sound in gas \(v=\sqrt{\dfrac{\gamma \mathrm{RT}}{\mathrm{M}}}\) Since the temperature is same for both the gases, \(\begin{aligned}& \dfrac{v_{H e}}{v_{H_{2}}}=\sqrt{\dfrac{\gamma_{H e} M_{H_{2}}}{\gamma_{H_{2}} M_{H e}}}=\sqrt{\dfrac{5 \times 5 \times 2}{3 \times 7 \times 4}}=\sqrt{\dfrac{25}{42}} \\& \Rightarrow \dfrac{v_{H_{2}}}{v_{H e}}=\dfrac{\sqrt{42}}{5}\end{aligned}\)
KCET - 2007
PHXI15:WAVES
354683
Sound velocity is maximum in
1 \({N_2}\)
2 \({H_2}\)
3 \({O_2}\)
4 \(He\)
Explanation:
\(v \propto \sqrt{\dfrac{\gamma}{M}}\) Since \(\dfrac{\gamma}{M}\) is maximum for \(H_{2}\) so sound velocity is maximum in \({H_2}.\)
PHXI15:WAVES
354684
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
354682
The ratio of the velocity of sound in hydrogen \((\gamma=7 / 5)\) to that in helium \((\gamma=5 / 3)\) at the same temperature is
1 \(\sqrt{\dfrac{5}{42}}\)
2 \(\sqrt{\dfrac{5}{21}}\)
3 \(\dfrac{\sqrt{42}}{5}\)
4 \(\dfrac{\sqrt{21}}{5}\)
Explanation:
Speed of sound in gas \(v=\sqrt{\dfrac{\gamma \mathrm{RT}}{\mathrm{M}}}\) Since the temperature is same for both the gases, \(\begin{aligned}& \dfrac{v_{H e}}{v_{H_{2}}}=\sqrt{\dfrac{\gamma_{H e} M_{H_{2}}}{\gamma_{H_{2}} M_{H e}}}=\sqrt{\dfrac{5 \times 5 \times 2}{3 \times 7 \times 4}}=\sqrt{\dfrac{25}{42}} \\& \Rightarrow \dfrac{v_{H_{2}}}{v_{H e}}=\dfrac{\sqrt{42}}{5}\end{aligned}\)
KCET - 2007
PHXI15:WAVES
354683
Sound velocity is maximum in
1 \({N_2}\)
2 \({H_2}\)
3 \({O_2}\)
4 \(He\)
Explanation:
\(v \propto \sqrt{\dfrac{\gamma}{M}}\) Since \(\dfrac{\gamma}{M}\) is maximum for \(H_{2}\) so sound velocity is maximum in \({H_2}.\)
PHXI15:WAVES
354684
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
