The shorter part has the higher frequency by 1 Hz; the plausible pair matching beat = 1 Hz with whole-length fundamentals near 250 Hz is 250.5 (smaller) and 249.5 (longer).

Since hydrogen is much lighter than oxygen (density ratio ~16), the speed of sound in hydrogen is about 4 times that in oxygen, giving 4:1.

Longitudinal (compressional) waves have particle motion parallel to wave propagation; hence 'Longitudinal waves' is the standard term.

Beat frequency = 16/20 = 0.8 Hz; using f = v/4L for closed pipes and the difference between v/(4·1.00) and v/(4·1.01) yields the velocity (given here as option B per provided answer key).

f ∝ (1/2L)√(T/μ); halving length gives factor 2, doubling thickness (diameter) makes area ×4 so μ×4, and tension ×1/4; net factor 2·√((1/4)/(4))=2·(1/4)=1/2, so 500 Hz → 250 Hz.

Moist air has lighter water vapour molecules replacing heavier nitrogen/oxygen, reducing mean molecular mass and increasing sound speed, so V_m > V_d.

A shift toward the violet (shorter wavelength) is a blueshift, indicating the star is approaching Earth.

Noise levels are measured in decibels (dB), a logarithmic unit measuring sound intensity.

At the same temperature the speed of sound decreases with increasing molar mass; SO2 has the largest molar mass among the options, so it gives the lowest speed.

Mass per unit length μ ∝ r², so μ1:μ2 = 1:4 and f ∝ 1/√μ; hence f1:f2 = √(μ2/μ1) = 2:1.