Advertisements
Advertisements
प्रश्न
Use the formula `v = sqrt((gamma P)/rho)` to explain why the speed of sound in air increases with humidity.
Advertisements
उत्तर १
Let `"v"_"m" and "v"_"d"` be the speeds of sound in moist air and dry air respectively.
Let `rho_"m"` and `rho_"d"` be the densities of moist air and dry air respectively.
Take the relation:
`"v" = sqrt((gamma "P")/rho)`
Hence, the speed of sound in moist air is:
`"v"_"m" = sqrt((gamma "P")/rho_"m")` ....(i)
And the speed of sound in dry air is:
`"v"_"d" = sqrt((gamma "P")/rho_"d")` ...(ii)
On dividing equations (i) and (ii), we get:
`"v"_"m"/"v"_"d" = sqrt((gamma"P")/rho_"m" xx rho_"d"/(gamma"P")) = sqrt(rho_"d"/rho_"m")`
However, the presence of water vapour reduces the density of air, i.e.,
`rho_"d" < rho_"m"`
`:. v_"m" > v_"d"`
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.
उत्तर २
We are given that `"v" = sqrt((gamma "p")/rho)`
We know PV = nRT (For n moles of ideal gas)
`=> "PV" = "m"/"M" "RT"`
where m is the total mass and M is the molecular mass of the gas
`:. "P" = "m"/"M" * "RT"/"M" = (rho "RT")/"M"`
`=> "P"/rho = "RT"/"M"`
Increase in humidity decrease the effective density of air. Therefore the velocity `("v" prop 1/sqrtrho)` increase.
APPEARS IN
संबंधित प्रश्न
A hospital uses an ultrasonic scanner to locate tumours in a tissue. What is the wavelength of sound in the tissue in which the speed of sound is 1.7 km s–1? The operating frequency of the scanner is 4.2 MHz.
A steel rod 100 cm long is clamped at its middle. The fundamental frequency of longitudinal vibrations of the rod is given to be 2.53 kHz. What is the speed of sound in steel?
A train, standing at the outer signal of a railway station blows a whistle of frequency 400 Hz in still air. (i) What is the frequency of the whistle for a platform observer when the train (a) approaches the platform with a speed of 10 m s–1, (b) recedes from the platform with a speed of 10 m s–1? (ii) What is the speed of sound in each case? The speed of sound in still air can be taken as 340 m s–1.
Velocity of sound in air is 332 m s−1. Its velocity in vacuum will be
A wave pulse, travelling on a two-piece string, gets partially reflected and partially transmitted at the junction. The reflected wave is inverted in shape as compared to the incident one. If the incident wave has wavelength λ and the transmitted wave λ'
Two wave pulses travel in opposite directions on a string and approach each other. The shape of one pulse is inverted with respect to the other.
Two waves of equal amplitude A, and equal frequency travel in the same direction in a medium. The amplitude of the resultant wave is
A sonometer wire of length l vibrates in fundamental mode when excited by a tuning fork of frequency 416. Hz. If the length is doubled keeping other things same, the string will ______.
Two waves, travelling in the same direction through the same region, have equal frequencies, wavelengths and amplitudes. If the amplitude of each wave is 4 mm and the phase difference between the waves is 90°, what is the resultant amplitude?
The equation for the vibration of a string, fixed at both ends vibrating in its third harmonic, is given by
\[y = \left( 0 \cdot 4 cm \right) \sin\left[ \left( 0 \cdot 314 {cm}^{- 1} \right) x \right] \cos \left[ \left( 600\pi s^{- 1} \right) t \right]\]
(a) What is the frequency of vibration? (b) What are the positions of the nodes? (c) What is the length of the string? (d) What is the wavelength and the speed of two travelling waves that can interfere to give this vibration?
A 40 cm wire having a mass of 3⋅2 g is stretched between two fixed supports 40⋅05 cm apart. In its fundamental mode, the wire vibrates at 220 Hz. If the area of cross section of the wire is 1⋅0 mm2, find its Young modulus.
The string of a guitar is 80 cm long and has a fundamental frequency of 112 Hz. If a guitarist wishes to produce a frequency of 160 Hz, where should the person press the string?
Use the formula `v = sqrt((gamma P)/rho)` to explain why the speed of sound in air is independent of pressure.
For the travelling harmonic wave
y (x, t) = 2.0 cos 2π (10t – 0.0080x + 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 4 m.
For the travelling harmonic wave
y (x, t) = 2.0 cos 2π (10t – 0.0080x + 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 0.5 m.
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 is in s. The positive direction of x is from left to right.
- The wave is travelling from right to left.
- The speed of the wave is 20 m/s.
- Frequency of the wave is 5.7 Hz.
- The least distance between two successive crests in the wave is 2.5 cm.
Speed of sound waves in a fluid depends upon ______.
- directty on density of the medium.
- square of Bulk modulus of the medium.
- inversly on the square root of density.
- directly on the square root of bulk modulus of the medium.
The amplitude of wave disturbance propagating in the positive x-direction given is by `1/(1 + x)^2` at time t = 0 and `1/(1 + (x - 2)^2)` at t = 1 s, where x and y are in 2 metres. The shape of wave does not change during the propagation. The velocity of the wave will be ______ m/s.
Two perfectly identical wires kept under tension are in unison. When the tension in the wire is increased by 1% then on sounding them together 3 beats are heard in 2 seconds. What is the frequency of each wire?
