The total distance traveled by the sound is d = speed × time = 340 m/s × 5 s = 1700 meters. Since the sound must travel to the mountain and back to the source to create an echo, the distance to the mountain is half the total distance: 1700 / 2 = 850 meters, which is 0.85 km.

The total distance traveled by the sound wave is speed multiplied by time (342 m/s * 3 s = 1026 m). Since an echo requires the sound to travel to the surface and back, the distance to the reflecting surface is half of the total distance: 1026 m / 2 = 513 meters.

In a longitudinal wave, such as sound, particles oscillate parallel to the direction of wave propagation. A compression is a region where particles are pushed closer together, resulting in higher local density and pressure, alternating with rarefactions where density is lower.

The speed of sound in a gas is inversely proportional to the square root of its molar mass. Since the molar mass of hydrogen (H2) is approximately 2 g/mol and oxygen (O2) is 32 g/mol, the ratio of speeds is the square root of (32/2), which equals the square root of 16, resulting in a factor of 4.

The human ear can typically detect sounds in the frequency range of 20 Hz to 20,000 Hz. Sounds with frequencies below this lower threshold of 20 Hz are defined as infrasonic. These low-frequency waves are often produced by natural phenomena like earthquakes or volcanic eruptions.

The human auditory system is capable of perceiving sound frequencies ranging from approximately 20 Hz to 20,000 Hz. An oscillation of 20,000 times per second corresponds to 20,000 Hz, which is generally considered the upper threshold of human hearing for young, healthy individuals.

A microphone is a transducer that converts sound waves (mechanical energy) into electrical signals. It typically uses a diaphragm that vibrates in response to sound pressure, which then induces an electrical current or voltage change. This process is the inverse of a speaker, which converts electrical signals back into sound energy. Microphones are essential components in recording, telecommunications, and public address systems.

The speed of sound in air is temperature-dependent because the kinetic energy of gas molecules increases with temperature, facilitating faster wave propagation. The standard linear approximation for this relationship is an increase of approximately 0.61 meters per second for every degree Celsius increase in temperature near room conditions.

The speed of sound depends on the density and the elastic properties of the medium. Generally, sound travels fastest in solids because the particles are more closely packed and have stronger intermolecular bonds compared to liquids and gases. Among the choices provided, copper is a solid, while water, air, and ammonia are liquids or gases, making copper the fastest medium.

Sound waves are characterized by physical properties such as amplitude (loudness), frequency/time period (pitch), and speed (velocity). While density is a property of the medium through which sound travels, it is not a characteristic of the wave itself. The wave propagates through the medium, but the density of the medium is an external factor.