Velocity of Sound in Air - Viva Questions

The following are a few commonly asked questions for the experiment, where you measure the speed of sound using CRO.

What are the factors on which the velocity/speed of sound depends on?
A. The speed of sound varies from medium to medium. It depends upon the properties of the medium such as it’s elasticity, and density. It also depends on temperature.
How does the speed of sound depend on Density and Elasticity?
A. The speed of sound is given by the following relation,
$v=\sqrt{\frac{K_s}{\rho}}$
where
$v$ is the speed,
$K_s$ is the elasticity of the medium, and
$\rho$ is the density of the medium.
Thus the speed of sound increases with the stiffness (the resistance of an elastic body to deformation by an applied force) of the material, and decreases with increase in density. For ideal gases the bulk modulus K is simply the gas pressure multiplied by the dimensionless adiabatic index, which is about 1.4 for air under normal conditions of pressure and temperature.
How does the speed of sound depend upon temperature?
A. Speed of sound is directly proportional to temperature. As the temperature increases, the the density decreases, and since the velocity is inversely proportional to the square root of density, as seen in the equation above, the speed of sound increases with increase in temperature.
The dependence of speed of sound on temperature in dry air is given by the following relation:

For an ideal gas,

where
- γ is the adiabatic index also known as the isentropic expansion factor. It is the ratio of specific heats of a gas at a constant-pressure to a gas at a constant-volume $\frac{C_p}{C_v}$ , and arises because a classical sound wave induces an adiabatic compression, in which the heat of the compression does not have enough time to escape the pressure pulse, and thus contributes to the pressure induced by the compression;
- p is the pressure;
- ρ is the density.
Using the ideal gas law to replace p with nRT/V, and replacing ρ with nM/V, the equation for an ideal gas becomes
$v=\sqrt{\gamma\frac{p}{\rho}}=\sqrt{\gamma \frac{RT}{M}}=\sqrt{\gamma \frac{kT}{m}}$

where
- v is the speed of sound in an ideal gas;
- R (approximately 8.314,5 J · mol⁻¹ · K⁻¹) is the molar gas constant(universal gas constant);
- k is the Boltzmann constant;
- γ (gamma) is the adiabatic index. At room temperature, where thermal energy is fully partitioned into rotation (rotations are fully excited) but quantum effects prevent excitation of vibrational modes, the value is 7/5 = 1.400 for diatomic molecules, according to kinetic theory. Gamma is actually experimentally measured over a range from 1.399,1 to 1.403 at 0 °C, for air. Gamma is exactly 5/3 = 1.6667 for monatomic gases such as noble gases;
- T is the absolute temperature;
- M is the molar mass of the gas. The mean molar mass for dry air is about 0.028,964,5 kg/mol;
- n is the number of moles;
- m is the mass of a single molecule.
Therefore, it is evident that assuming an ideal gas, the speed of sound v depends on temperature only, not on the pressure or density (since these change in lockstep for a given temperature and cancel out). Air is also almost an ideal gas.
How does the speed of sound change with humidity?
A. The speed of sound increases with increase in humidity as the water molecules are lighter than the air molecules and hence the density decreases, thereby increasing the speed. The increase in speed, however, is very small, so for most everyday purposes you can ignore it. In room temperature air at sea level, for example, sound travels about 0.35 percent faster in 100 percent humidity (very humid air) than it does in 0 percent humidity (completely dry air). The “rigidity” of air or its elastic modulus does not change with humidity.
What happens to the speed of sound when you go higher in altitude?
A. As one goes higher in altitude, the
Why does sound travel faster in solids than liquids or gases?
A. Sound travels faster in solids as they have a higher elasticity. The speed of sound increases with the stiffness (the resistance of an elastic body to deformation by an applied force) of the material, and decreases with increase in density. Though, solids are denser than liquids and gases, but still the increase in stiffness is far greater than the increase in density and more than compensates for it.
Derive the equation of the Lissajous figure for two signals of same frequency, phase difference φ and different amplitudes.
Show that the Lissajous figure is a straight line for phase angle φ = π,2π… .
What does the ratio of frequencies determine?
What is an audio transformer?
A. As their name suggests, audio transformers are designed to operate within the audio band of frequencies and as have applications in the input stage (microphones), output stage (loudspeakers), inter-stage coupling as well as impedance matching of amplifiers.
How does the audio transformer perform impedance matching?
A.One of the main applications for audio frequency transformers is in impedance matching. Audio transformers are ideal for balancing amplifiers and loads together that have different input/output impedances in order to achieve maximum power transfer.For example, a typical loudspeaker impedance ranges from 4 to 16 ohms whereas the impedance of a transistor amplifiers output stage can be several hundred ohms. A classic example of this is the LT700 Audio Transformer which can be used in the output stage of an amplifier to drive a loudspeaker.We know that for a transformer, the ratio between the number of coil turns on the primary winding (N_P) to the number of coil turns on the secondary winding (N_S) is called the “turns ratio”. Since the same amount of voltage is induced within each single coil turn of both windings, the primary to secondary voltage ratio (V_P/V_S) will therefore be the same value as the turns ratio.Impedance matching audio transformers always give their impedance ratio value from one winding to another by the square of the their turns ratio. That is, their impedance ratio is equal to its turns ratio squared and also its primary to secondary voltage ratio squared as shown.
Audio Transformer Impedance Ratio

$\frac{Z_p}{Z_s}=\left(\frac{N_p}{N_s}\right)^2=\left(\frac{V_p}{V_s}\right)^2$

Where Z_P is the primary winding impedance, Z_S is the secondary winding impedance, (N_P/N_S) is the transformers turns ratio, and (V_P/V_S) is the transformers voltage ratio.

So for instance, an impedance matching audio transformer that has a turns ratio (or voltage ratio) of say 2:1, will have an impedance ratio of 4:1.

References:

Ph.D. researcher at Friedrich-Schiller University Jena, Germany. I’m a physicist specializing in computational material science. I write efficient codes for simulating light-matter interactions at atomic scales. I like to develop Physics, DFT, and Machine Learning related apps and software from time to time. Can code in most of the popular languages. I like to share my knowledge in Physics and applications using this Blog and a YouTube channel.

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