Why are sound waves longitudinal waves and not transverse waves?
Answer: Sound waves in gases and liquids are longitudinal waves because the particles of the medium vibrate to and fro parallel to the direction in which the sound wave travels. A vibrating sound source produces successive compressions and rarefactions in the medium, and these pressure disturbances propagate through the medium.
In gases and liquids, the medium cannot sustain a shear restoring force for bulk transverse deformation. Therefore, a mechanical transverse wave cannot normally propagate through the bulk of a fluid. Sound consequently travels through fluids mainly as a longitudinal wave involving variations in pressure and density.
Solids can sustain both longitudinal and shear restoring forces. Therefore, mechanical longitudinal and transverse waves can propagate through solids. However, ordinary sound propagation through air is longitudinal.
Why can sound waves not travel through vacuum?
Answer: Sound is a mechanical wave and therefore requires a material medium for its propagation. When a sound source vibrates, it causes neighbouring particles of the medium to oscillate. These particles exert forces on adjacent particles and transfer the disturbance from one region to another.
A vacuum contains essentially no material particles that can participate in this process. Therefore, there are no particles available to transmit the mechanical disturbance from the source to another location.
Hence, sound cannot travel through vacuum. This is different from electromagnetic waves such as light, radio waves and X-rays, which do not require a material medium and can propagate through vacuum.
Why is the speed of sound maximum in solids?
Answer: The speed of a longitudinal wave depends mainly on the elasticity and density of the medium. In general, the speed can be represented by:
Here, \(E\) represents the appropriate elastic modulus of the medium and \(\rho\) represents its density.
Solids generally have a very high elastic modulus. This means that when a solid is compressed or deformed, it develops a strong restoring force. Therefore, a disturbance produced at one point can be transmitted rapidly to neighbouring particles.
Although solids generally have greater density than liquids and gases, their much greater elasticity more than compensates for the increase in density. As a result, the speed of sound is generally greatest in solids.
Why is the speed of sound least in gases?
Answer: The speed of sound depends on the ratio of the elastic restoring property of the medium to its density. Gases have a much lower effective stiffness than solids and liquids, so pressure disturbances propagate through them more slowly.
For an ideal gas, the speed of sound is given by the Newton–Laplace relation:
Here, \(P\) is the pressure, \(\rho\) is the density and \(\gamma\) is the ratio of specific heats. The relatively low stiffness of gases results in a much lower wave speed than in solids and liquids.
Therefore, under ordinary conditions, the speed of sound follows the order:
Why does increasing the frequency of a wave not necessarily increase its speed in the same medium?
Answer: For a wave travelling through a given non-dispersive medium under unchanged physical conditions, the wave speed is determined primarily by the properties of the medium rather than by the frequency of the source.
The relationship between wave velocity, frequency and wavelength is:
If the frequency is increased while the wave travels through the same non-dispersive medium, its wavelength decreases correspondingly so that the wave speed remains unchanged.
Therefore, increasing frequency does not necessarily increase wave speed. In a non-dispersive medium, different frequencies can travel with the same speed.
In a dispersive medium, however, wave speed can depend on frequency. Therefore, the statement about unchanged wave speed applies specifically to the non-dispersive case.
Why does a progressive wave transfer energy from one place to another?
Answer: A progressive wave is a travelling disturbance that continuously moves through the medium. When one particle of the medium is disturbed, it exerts a force on neighbouring particles and transfers energy to them. The neighbouring particles then transfer energy to the particles farther along the medium.
Therefore, the disturbance and energy progressively travel from one region to another, even though the particles of the medium generally oscillate about their equilibrium positions rather than travelling with the wave.
Why do different particles of a progressive wave have different phases?
Answer: In a progressive wave, the disturbance reaches different particles at different times. Therefore, particles at different positions generally do not execute their oscillations simultaneously.
For a wave travelling in the positive \(x\)-direction, a typical wave equation is:
The phase of a particle at position \(x\) is:
Therefore, at the same instant, particles at different positions have different values of phase because the term \(kx\) changes with position.
For two particles separated by a distance \(\Delta x\), their phase difference is:
Thus, the phase of a particle in a progressive wave depends on both time and position.
Why does the equation of a progressive wave contain both position and time?
Answer: A progressive wave is a disturbance that changes with both position and time. As the wave travels, different particles at different positions experience the disturbance at different times.
A sinusoidal progressive wave travelling in the positive \(x\)-direction can be written as:
Here, \(t\) describes the time variation of the particle’s oscillation, while \(x\) describes how the disturbance changes from one position to another.
The presence of both \(x\) and \(t\) is therefore essential for describing a travelling wave. If the position is fixed, the equation describes the oscillation of one particular particle with time. If the time is fixed, it describes the shape of the wave at that instant along the medium.
Why is the particle velocity zero at the extreme positions of a wave?
Answer: The particles of a medium execute oscillatory motion as a progressive wave passes through them. At the extreme positions of their oscillation, a particle momentarily comes to rest before reversing its direction of motion.
For a progressive wave:
The particle velocity is obtained by differentiating displacement with respect to time:
At an extreme position, \(y=\pm A\). Therefore, the cosine factor becomes zero and:
Hence, a particle has zero instantaneous velocity at its extreme positions and maximum velocity while passing through its equilibrium position.
Why does the resultant amplitude change when two waves interfere?
Answer: When two waves meet at the same point, their displacements combine according to the principle of superposition. The resultant displacement is the algebraic sum of the individual displacements.
The resultant amplitude depends on the phase difference between the two waves. For two waves having amplitudes \(A_1\) and \(A_2\), the resultant amplitude is:
When the waves are in phase, \(\phi=0\), and constructive interference occurs:
When the waves are completely out of phase, \(\phi=\pi\), and destructive interference occurs:
Thus, the resultant amplitude changes because the relative phase between the interfering waves determines whether their displacements reinforce or cancel one another.