For a human to distinguish an echo from the original sound, the time delay must be at least 0.1 seconds. Given the speed of sound is approximately 340 m/s, the total distance traveled is 34 meters. Since the sound must travel to the obstacle and back, the minimum distance to the obstacle is half of that, which is 17 meters.

The speed of sound in a solid depends on its elastic modulus and density. Aluminium has a high ratio of Young's modulus to density compared to iron, steel, and brass, resulting in a higher longitudinal wave velocity. At 25°C, the speed of sound in aluminium is approximately 6320 m/s, which is higher than the other listed metals.

Frequency is related to the pitch of the sound. Women and children generally have shorter vocal cords, which vibrate at a higher frequency, resulting in a higher pitch compared to the deeper, lower-frequency voices of adult men.

When a diaphragm vibrates, it creates periodic compressions and rarefactions in the surrounding air molecules. These pressure disturbances propagate through the medium as longitudinal mechanical waves, which are perceived by the human ear as sound waves.

The Hertz (Hz) is the standard SI unit for frequency, defined as one cycle per second. It is named after the physicist Heinrich Hertz, who made significant contributions to the study of electromagnetism and wave phenomena.

A microphone acts as a transducer that captures sound waves (mechanical energy) and converts them into corresponding electrical signals. This process is essential for audio recording, telecommunications, and sound amplification systems, distinguishing it from devices like loudspeakers which perform the reverse operation.

Using the wave equation v = f * λ, we rearrange to find frequency: f = v / λ. Converting 1.5 cm to 0.015 m, we get f = 339 / 0.015 = 22600 Hz.

The speed of sound in a gas is directly proportional to the square root of its absolute temperature. As temperature increases, the kinetic energy of the gas molecules increases, leading to more frequent collisions and faster transmission of the sound wave through the medium.

Sound is a mechanical wave that requires a material medium to travel. It can propagate through solids, liquids, and gases because these media possess the necessary elasticity and inertia to transmit the mechanical vibrations from particle to particle. Sound cannot travel through a vacuum.

Audible waves fall within the range of 20 Hz to 20,000 Hz (a-2). Infrasonic waves are those with frequencies below 20 Hz (b-1). Ultrasonic waves are those with frequencies above 20,000 Hz (c-3). Therefore, the correct matching is a-2, b-1, and c-3.