Q.On increasing the temperature of air by 1°C, velocity of sound in it increases by

When a sound wave travels from air into water, its frequency stays the same; only its speed and wavelength change.

The frequency of a wave is determined by the source producing it — every particle in the new medium is forced to oscillate at the same rate as the source, so the frequency cannot change just because the medium changes. However, the wave's speed does change (sound travels much faster in water, ~1480 m/s, than in air, ~340 m/s, because water is denser and less compressible in the relevan …

By the Newton-Laplace formula v = √(γP/ρ), the ratio P/ρ stays constant at a given temperature (since ρ is proportional to P for a fixed amount of gas), so the speed of sound in a gas does not change with pressure alone.

The speed of sound in a gas is given by the Newton-Laplace formula:

v = √(γP/ρ)

where P is pressure, ρ is density, and γ = Cp/Cv.

From the ideal gas equation, PV = nRT, so PM = ρRT (M = molar mass), giving:

P/ρ = RT/M

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Speed of sound in air increases by about 0.61 m/s per degree C. Answer (D).

The speed of sound in air varies with temperature approximately as v = 331 + 0.61 t (m/s), with t in degrees C.

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Speed of sound in a gas is independent of pressure, although it does depend on temperature and (weakly) on humidity.

Speed of sound in a gas: $v = \sqrt{\dfrac{\gamma P}{\rho}}$

For an ideal gas at fixed temperature, density $\rho$ is directly proportional to pressure $P$ (from $PV=nRT \Rightarrow \rho = PM/RT$), so the ratio $P/\rho$ stays constant even if $P$ changes — meaning $v$ does not change with pressure at constant temperature.

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The speed of sound in air is the same at 4 atm and 1 atm — ratio 1:1.

Speed of sound: $v = \sqrt{\gamma P/\rho}$. For a fixed mass of gas at a given (unchanged) temperature, density is proportional to pressure ($\rho \propto P$), so $P/\rho$ is a constant independent of the actual pressure value. Hence $v$ is unaffected by a chang …

The Assertion is true, but the Reason is false — light is much faster than sound, not slower.

Assertion: The flash of lightning is seen before the sound of thunder is heard — this is TRUE. Both the flash and the thunder are produced at essentially the same instant (the electrical discharge), but they reach an observer at very different times because they travel at very different speeds.

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Speed of sound in a gas increases with temperature, since $v\propto\sqrt T$.

The speed of sound in a gas is given by Laplace's formula, $v=\sqrt{\dfrac{\gamma P}{\rho}}=\sqrt{\dfrac{\gamma RT}{M}}$ (using the ideal gas law), where $T$ is the absolute temperature. Since …

Speed of sound depends on the medium's elasticity and density (v = √(E/ρ) for solids); solids like iron have by far the highest speed of sound among solids, liquids and gases.

Sound needs a material medium to travel (it's a mechanical wave), so it cannot travel through a vacuum at all — this immediately rules out option (c).

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Sound travels fastest in solids because their elasticity (bulk/rigidity modulus) is far higher than that of liquids or gases.

The speed of sound in a medium is given generally by $v = \sqrt{E/\rho}$, where $E$ is the relevant modulus of elasticity of the medium and $\rho$ is its density. Although solids are also denser than gases, their elastic modulus is enormously larger — solids strongly resist both compression and shear — and this dominates the ratio $E/\rho$. …

Speed of sound in a gas is v = sqrt(gamma RT/M). Humid air has a lower effective molar mass M than dry air (water vapour molecules are lighter than N2/O2), so sound speed INCREASES with humidity; it is essentially independent of pressure at constant temperature, and strongly dependent on (increases with) temperature.

The speed of sound in an ideal gas is given by:

v = sqrt(gamma R T / M)

where gamma is the adiabatic index, R the gas constant, T the absolute temperature, and M the molar mass of the gas.

Checking each option:

(1) 'independent of temperature' -- FALSE; v is proportional to sqrt(T), so sound speed clearly depends on (increases with) temperature.

(2) 'increases with increase in pressure' -- FALSE; at constant temperature, increasing pressure also proportionally increases density, and these effects cancel in the formula v = sqrt(gamma P/rho) -- sound speed is essentially independent of pressure at constant T. …

Speed of sound in air depends strongly on temperature (increasing with it) and also increases with humidity, because moist air has a lower density than dry air.

The speed of sound in a gas is given by v = sqrt(gamma P / rho) (or equivalently, for an ideal gas, v = sqrt(gamma R T / M)).

• Temperature: v increases with increasing temperature (since v is proportional to sqrt(T)), so option (a) 'independent of temperature' is wrong.
• Pressure: at constant temperature, P and rho both change proportionally for a given amount of gas (P/rho is roughly constant for an ideal gas at fixed T), so speed of sound is essentially independent of pressure alone, ruling out option (b). …