Advertisements
Advertisements
प्रश्न
Helium gas is filled in two identical bottles A and B. The mass of the gas in the two bottles is 10 gm and 40 gm respectively. If the speed of sound is the same in both bottles, what conclusions will you draw?
Advertisements
उत्तर
Let the gas filled bottles be A and B respectively.
Mass of the gas in bottle A = 10 g
Mass of gas in bottle B = 40 g
The velocity of sound in gas is related to the density of gas as
`v ∝ 1/sqrt(ρ)` ...... (i)
and the velocity of sound in a gas is related to the temperature of the gas as
`v ∝ sqrt(T)` ...... (ii)
Combining (i) and (ii), we get
`v ∝ sqrt(T)/sqrt(ρ)`
The bottles are identical, which means the volumes of the gases are equal. Let the volume of the bottle be V. Let M1 and M2 be the masses of gases in bottles A and B, respectively and v1 and v2 be the velocity of the sound in the two bottles, respectively. Also, let T1 and T2 be their respective temperatures. Therefore,
`v_1/v_2 = (sqrt(M_2/V) sqrt(T_1))/(sqrt(M_1/V) sqrt(T_2))`
Now, given that, `"v"_1 = "v"_2`
⇒ `sqrt(M_1)sqrt(T_2) = sqrt(M_2)sqrt(T_1)`
or , `T_2 = (M_2T_1)/M_1`
Given , `M_1 = 10 "g" , M_2 = 40 "g"`
= `T_2 = (40T_1)/10 = 4T_1`
Thus, it can be concluded that the temperature of bottle B is 4 times the temperature of A.
APPEARS IN
संबंधित प्रश्न
Two children are at opposite ends of an aluminium rod. One strikes the end of the rod with a stone. Find the ratio of times taken by the sound wave in air and in aluminium to reach the second child.
A sound wave travels at a speed of 339 m s−1. If its wavelength is 1.5 cm, what is the frequency of the wave? Will it be audible?
A stone is dropped from the top of a tower 500 m high into a pond of water at the base of the tower. When is the splash heard at the top? Given, g = 10 m s−2 and speed of sound = 340 m s−1.
Write true or false for a given statement.
Sound can travel in a vacuum.
Describe an experiment to show that sound can travel in water.
Write the approximate speed of sound in air.
Which of the following is the speed of sound in copper and which in aluminium?
(a) 5100 m/s
(b) 1500 m/s
(c) 3750 m/s
A worker lives at a distance of 1.32 km from the factory. If the speed of sound in air be 330 m/s, how much time will the sound of factory siren take to reach the worker?
A man is kidnapped, blindfolded and imprisoned in a big room. How could the man tell if he was in : a village
The speed of highly penetrating ultrasonic waves is :
The incidence of ______ in daily life shows that the velocity of sound is less than the velocity of light.
Hydrogen gas is filled in two identical bottles, A and B, at the same temperature. The mass of hydrogen in the two bottles is 12 gm and 48 gm respectively. In which bottle will sound travel faster? How many times be as fast as the other?
Velocity of sound in a gaseous medium is 330 ms–1. If the pressure is increased by 4 times without causing a change in the temperature, the velocity of sound in the gas is
The velocity of sound in air at a particular temperature is 330 ms–1. What will be its value when temperature is doubled and the pressure is halved?
The velocity of sound is independent of temperature.
Sound travels faster in ______ and slower in ______.
Assertion: The speed of sound in air is less than the speed of sound in solid.
Reason: If we increase the temperature of medium, the speed of sound increases in any medium.
The speed of sound in a gaseous medium depends on the nature of the gas.
Numerical problems:
A Sound wave travels at a speed of 344 ms-1. If the wavelength is 1.5 cm, what is the frequency of the Wave? Will it be audible?
