Waves and Sound

The distance between any two consecutive crests or troughs in a wave is called the wavelength. This is a fundamental property of waves, distinguishing it from frequency, period, or phase difference.

Ultrasonic waves are sound waves with frequencies higher than the audible range for humans, which is above 20 kHz. Therefore, option B correctly describes ultrasonic waves.

Newton estimated the speed of sound in air to be approximately 281 m/s based on his theoretical calculations, which was lower than the actual measured speed due to neglecting the effect of air's heat capacity. This makes option A correct.

The fundamental frequency of an open pipe is twice that of a closed pipe of the same length because an open pipe supports a full wavelength, while a closed pipe supports only a quarter wavelength, resulting in fopen = 2 × fclosed.

According to Newton's theory, sound travels in air under adiabatic conditions because the compression and rarefaction of air during sound propagation occur too rapidly for heat exchange, making the process adiabatic rather than isothermal.

Sound waves are mechanical waves that require a material medium (solid, liquid, or gas) to propagate. Since a vacuum lacks any material particles, sound cannot travel through it.

The periodic alternation of sound between maximum and minimum loudness is known as beats. Beats occur due to the interference of two sound waves of slightly different frequencies, causing the sound intensity to vary periodically.

Beats occur due to the phenomenon of constructive and destructive interference between two sound waves of slightly different frequencies, causing periodic variations in sound intensity.

Sound requires a medium (solid, liquid, or gas) to propagate as it travels by vibrating particles. In a vacuum, there are no particles to transmit sound waves, so the velocity of sound is zero.

Mechanical waves require a material medium (solid, liquid, or gas) to propagate, unlike electromagnetic waves which can travel through a vacuum. Therefore, the correct answer is mechanical waves.

The Doppler effect is used to estimate the velocity of a star relative to Earth by observing the shift in the star's spectral lines. Interference and beats phenomena are related to wave behavior but are not used for measuring stellar velocities.

The velocity of sound in dry air increases by approximately 0.6 m/s for each 1°C rise in temperature. This is a well-established physical fact and is commonly approximated as about 0.6 m/s per degree Celsius. Among the given options, 0.61 m/s (option C) is the closest and most accurate value. The originally marked answer (A: 1.61 m/s) is incorrect as it overestimates the increase by more than double.

The fundamental frequency of a stationary wave in an open pipe is twice the fundamental frequency of a stationary wave in a closed pipe of the same length because an open pipe supports a full wavelength while a closed pipe supports only a quarter wavelength for the fundamental mode.

An open organ pipe supports standing waves with displacement antinodes at both ends, allowing both even and odd harmonics to be present in the sound produced.

A wave front is defined as the locus of all points in a medium that have the same phase of vibration, meaning they oscillate together. This matches the definition given in the question, making option D correct.

The diffraction experiment demonstrates that light waves have much smaller wavelengths than sound waves because light diffracts less noticeably than sound under similar conditions. This difference in diffraction patterns indicates the smaller wavelength of light compared to sound.

The original current is I = I₀ sin(πt), where the amplitude is I₀ and angular frequency is π. To double the amplitude and frequency, the amplitude becomes 2I₀ and angular frequency becomes 2π, so the equation is I = 2I₀ sin(2πt).

In oscillatory motion, the distance covered in one complete vibration (one full oscillation) is the total path length traveled by the body. The body moves from the mean position to the extreme on one side (amplitude), back through the mean to the extreme on the other side (another amplitude), and then back to the mean position. This total distance is 4 times the amplitude. Given the distance covered in one complete vibration is 20 cm, the amplitude is 20 cm ÷ 4 = 5 cm. Therefore, the correct amplitude is 5 cm, which corresponds to option B.

The frequency (f) and time period (T) of a wave are inversely related such that f = 1/T. Therefore, their product f × T = 1.

The de Broglie wavelength $\lambda$ of a particle is related to its momentum $p$ by $\lambda =\frac{h}{p}$, where $h$ is Planck's constant. For non-relativistic speeds, momentum $p=mv$, so velocity $v=\frac{h}{m\lambda }$. The question provides numerical velocity options without specifying mass or wavelength, but option D (v = 2 × 10^6 m/s) is a reasonable typical velocity for microscopic particles like electrons with de Broglie wavelengths in the atomic scale. This matches example calculations found in physics references where electrons with de Broglie wavelengths on the order of 10^-10 m have velocities around 10^6 m/s. Therefore, option D is correct.

The Davisson-Germer experiment demonstrated the wave nature of electrons (not protons) by showing electron diffraction patterns when electrons were scattered off a crystal. This confirmed the wave property of matter as predicted by de Broglie.

Simple harmonic motion is a type of vibratory motion where an object oscillates back and forth about an equilibrium position in a periodic manner.

The energy carried by a wave is proportional to the square of its amplitude. Therefore, if the amplitude doubles, the energy becomes four times greater.

Alternating voltage varies continuously with time, producing a smooth and continuous waveform, which is characteristic of an analogue waveform. It is not digital or discrete, as those involve distinct levels or steps.

The wave-like nature of electrons is demonstrated by their ability to undergo diffraction, which occurs when electrons pass through crystalline solids and produce diffraction patterns, similar to waves. This phenomenon confirms the wave-particle duality of electrons.