Advertisements
Advertisements
Question
Consider a mixture of 2 mol of helium and 4 mol of oxygen. Compute the speed of sound in this gas mixture at 300 K.
Advertisements
Solution
Number of molecules of helium = 2
Number of molecules of oxygen = 4
When helium and oxygen are mixed, hence the molecular weight of the mixture of gases is given by
`"M"_"mix" = [("n"_1"M"_1 + "n"_2"M"_2)/("n"_1 + "n"_2)]`
`= [(2 xx 4 + 4 xx 32)/(2 + 4)]`kg/mol
`= (8 + 128)/6`
`= 136/6` kg/mol
= 22.6 × 10-3 kg/mol
In addition, helium is monoatomic,
`"C"_("v"_2) = (2"R")/2`
Oxygen is diatomic `"C"_("v"_1) = (5"R")/2`
∴ For the mixture `("C"_"v")_"mix" = ("n"_1"C"_("v"_1) + "n"_2"C"_("v"_2))/("n"_1 + "n"_2)`
`("C"_"v")_"mix" = (2 xx 3/2 "R" + 4 xx 5/2 "R")/(2 + 4) = (13 "R")/6`
From Meyor's relation
`("C"_"p")_"mix" = ("C"_"v")_"mix" + "R"`
`("C"_"p")_"mix" = (13"R")/6 + "R" = (13"R" + "5R")/6 = (19"R")/6`
Ratio of specific heat capacitors of a mixture of gases is
`lambda_"mix" = "C"_"p"/"C"_"v" = ((19"R")/6)/((13"R")/6) = 19/13`
According to Laplace, the speed of sound in a gas is
v = `sqrt((lambda "RT")/("M"))`
v = `sqrt(19/13 xx (8.31 xx 300)/(22.6 xx 10^-3))`
`= sqrt(28420.2/17.68 xx 10^4)`
= 4.009 × 102 m/s
= 400.9 m/s
∴ The speed of sound = 400.9 m/s
APPEARS IN
RELATED QUESTIONS
State the expression for apparent frequency when listener is stationary and source is moving towards the listener.
Answer briefly.
State the expression for apparent frequency when source of sound and listener are
- moving towards each other
- moving away from each other
The sound emitted from the siren of an ambulance has a frequency of 1500 Hz. The speed of sound is 340 m/s. Calculate the difference in frequencies heard by a stationary observer if the ambulance initially travels towards and then away from the observer at a speed of 30 m/s.
What is meant by the Doppler effect?
Discuss the following case-
Both are in motion
- Source and Observer approach each other
- Source and Observer resides from each other
- Source chases Observer
- Observer chases Source
A sound source and listener are both stationary and a strong wind is blowing. Is there a Doppler effect?
A bus is moving with a velocity of 5 m is towards a wall. The driver blows the horn of frequency 165 Hz. If the speed of sound in air is 335 m is, then after reflection of sound wave, the number of beats per second heard by the passengers in the bus will be ______.
An observer moves towards a stationary source of sound with a velocity one-fifth of the velocity of sound. The percentage increase in the apparent frequency heard by the observer will be ______.
The pitch of the whistle of an engine appears to drop to`(5/6)^"th"` of original value when it passes a stationary observer. If the speed of sound in air is 350 m/s then the speed of engine is ____________.
The difference between the apparent frequency of a stationary source of sound as perceived by the observer during its approach and recession is 2% of the frequency of the source. If the speed of sound in air is 300 ms–1, then the velocity of the observer is
