Round-trip time to each cliff is 1 s and 2 s, so distances are 165 m and 330 m; the width is the sum 165+330 = 495 m.

A tuning fork produces sound waves in air, which are longitudinal pressure waves; thus the waves produced in the air are longitudinal.

Intensity (power per unit area) has SI unit watts per square metre, W m^-2.

Initial unknown f satisfies |f-288|=4 so f=284 or 292; adding wax lowers its frequency and resulting beat |f' - 288|=2, which is consistent if original f=292 (decreasing to 290), so 292 cps is correct.

For an ideal gas at constant temperature the speed depends on temperature not pressure, so it remains approximately 300 m/s.

The envelope (amplitude factor) varies with angular frequency Δω/2, so its ordinary frequency is half the beat frequency (mathematically).

Laplace corrected Newton by assuming rapid sound propagation is adiabatic (no heat exchange) rather than isothermal.

Sound is a mechanical wave and requires a material medium (solid, liquid, or gas) to propagate.

Sound requires a material medium to propagate, so it cannot travel through vacuum and its speed there is zero.

At fixed temperature, sound speed in an ideal gas is essentially independent of pressure because both pressure and density change proportionally.