Class 11 Physics - Chapter Waves NCERT Solutions | Use the formula v = √ γP/&rh
Use the formula v = √ γP/ρ to explain why the speed of sound in air (a) is independent of pressure, (b) increases with temperature, (c) increases with humidity.
(a) Take the relation:
v = √ γP/ρ .... (i)
where density, ρ = Mass / Volume = M / V
Hense eqation one reduces to:
v = √ γPV/M ....(ii)
Now from the ideal gas equation for n = 1:
PV = RT
For constant T, PV = Constant
Since both M and γ are constants, v = Constant
Hence, at a constant temperature, the speed of sound in a gaseous medium is independent of the change in the pressure of the gas.
(b) Take the relation:
v = √ γP/ρ .... (i)
For one mole of an ideal gas, the gas equation can be written as:
PV = RT
P = RT / V … (ii)
Substituting equation (ii) in equation (i), we get:
v = √ γRT / Vρ = √γRT / M ....(iii)
Where, Mass, M = ρV is a constant
γ and R are also constants
We conclude from equation (iii) that v ∝ √T
Hence, the speed of sound in a gas is directly proportional to the square root of the temperature of the gaseous medium, i.e., the speed of the sound increases with an increase in the temperature of the gaseous medium and vice versa.
(c) Let Vm and Vd be the speeds of sound in moist air and dry air respectively.
Let ρm and ρd be the densities of moist air and dry air respectively.
Take the relation:
v = √ γP/ρ
Hence, the speed of sound in moist air is:
vm = √ γP/ρm .....(i)
And the speed of sound in dry air is:
vd = √ γP/ρd .....(ii)
On dividing equations (i) and (ii), we get:
However, the presence of water vapour reduces the density of air, i.e.,
ρd < ρm
therefore, Vm > Vd
Hence, the speed of sound in moist air is greater than it is in dry air. Thus, in a gaseous medium, the speed of sound increases with humidity.
More Questions From Class 11 Physics - Chapter Waves
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A transverse harmonic wave on a string is described by
y(x,t) = 3.0 sin [36t + 0.018x + π /4]
Where x and y are in cm and t in s. The positive direction of x is from left to right.
(a) Is this a travelling wave or a stationary wave? If it is travelling, what are the speed and direction of its propagation?
(b) What are its amplitude and frequency?
(c) What is the initial phase at the origin?
(d) What is the least distance between two successive crests in the wave?
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(b) Bats can ascertain distances, directions, nature, and sizes of the obstacles without any eyes,
(c) A violin note and sitar note may have the same frequency, yet we can distinguish between the two notes,
(d) Solids can support both longitudinal and transverse waves, but only longitudinal waves can propagate in gases, and
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A narrow sound pulse (for example, a short pip by a whistle) is sent across a medium.
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(b) If the pulse rate is 1 after every 20 s, (that is the whistle is blown for a split of second after every 20 s), is the frequency of the note produced by the whistle equal to or 0.05 Hz?
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For the travelling harmonic wave
y (x, t) = 2.0 cos 2π (10t - 0.0080 x + 0.35)
Where x and y are in cm and t in s. Calculate the phase difference between oscillatory motion of two points separated by a distance of
(a) 4 m,
(b) 0.5 m,
(c) λ / 2 ,
(d) 3λ / 4
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