Physics · Waves · NEET
No. This is the single most tested trap. From v = sqrt(gamma P / rho), it LOOKS like more pressure means faster sound. But at a fixed temperature, if you increase pressure you also increase density in the same proportion (Boyle's law: P is proportional to rho). So the ratio P/rho stays constant, and v does not change. Speed of sound is independent of pressure at constant temperature.
Use v = sqrt(gamma R T / M). Here R, gamma and M (molar mass) are constant for a given gas, so v is proportional to sqrt(T) with T in KELVIN. Higher temperature means gas molecules move faster and pass the disturbance along quicker. At 0 degrees C (273 K) sound in air is about 331 m/s; near room temperature it is about 343 m/s.
Yes, when you compare two DIFFERENT gases at the same temperature and pressure. From v = sqrt(gamma P / rho), a denser gas (larger rho) gives a smaller speed, so v is proportional to 1/sqrt(rho). That is why sound is much faster in light hydrogen or helium than in heavier CO2. But do NOT confuse this with squeezing the same gas harder, which changes P and rho together and leaves v unchanged.
Always Kelvin in the ratio v2/v1 = sqrt(T2/T1). Add 273 to any Celsius value first. If you use Celsius directly you will get a badly wrong answer. Convert 27 degrees C to 300 K, 0 degrees C to 273 K, and so on.
Near ordinary temperatures, the speed of sound in air rises by about 0.61 m/s for every 1 degree C rise. So v(t) is approximately 331 + 0.61 t, where t is in Celsius. This is an approximation of v proportional to sqrt(T) that works well only for everyday temperatures around 0 to 40 degrees C.
Faster. Water vapour (molar mass 18) is lighter than dry air (average molar mass about 29). Adding water vapour lowers the average density of the air, and since v is proportional to 1/sqrt(rho) at the same pressure, moist air carries sound slightly faster than dry air.
Try the real previous-year questions from this chapter — each with the answer and a full solution.
v = sqrt(gamma P / rho) = sqrt(gamma R T / M), where gamma is the ratio of specific heats, P is pressure, rho is density, T is absolute temperature in kelvin, R is the gas constant and M is the molar mass. This comes from Newton's formula corrected by Laplace using the adiabatic assumption.
Only temperature. For a fixed gas, gamma, R and M are constant, so v depends only on T through v proportional to sqrt(T). Pressure has no effect, and the density of that same gas changes only because temperature or pressure changed.
Sound speed is v = sqrt(elastic modulus / density). Solids have a very large elastic modulus (stiffness) compared with gases, and although they are denser, the huge rise in stiffness wins. So sound is fastest in solids, slower in liquids, and slowest in gases.
No. In a given medium at a given temperature the speed of sound is fixed and does not depend on the frequency, wavelength or loudness (amplitude) of the sound. A high note and a low note reach you at the same speed.
About 0.61 m/s for each 1 degree C rise near ordinary temperatures, giving the handy formula v is approximately 331 + 0.61 t m/s, with t in degrees Celsius.
