For producing node, the superposing wave must travel in the opposite direction (x term must have opposite sign) and its displacement must be negative. Hence the correct option is y=-asin⁡(ωt+kx)
Moreover,
y=y₁+y₂=asin⁡(ωt-kx)-asin⁡(ωt+kx)
y=-2acosωtsinkx
At x=0, y = 0. That is a node is formed.

v_He/v_(O2) = √(γ_He/γ_(O2) ×M_(O2)/M_He)=√((5/3)/(7/5)×32/4)=√(200/21)
=√9.52=3.086
v_He=3.086v_(O2)=3.086×460=1420m/s.

When the string vibrates in one segment,
L=ÊŽ/2
ÊŽ=2L=2×40=80cm.

L₁=10log⁡(I₁/I₀) L₂=10log⁡(I₂/I₀)
I₁-I₂=10log⁡(I₁/I₂)
20dB=10log⁡(I₁/I₂)
I₁/I₂ = 10² I₂=1/100×I₁.

v_H/v_O = √(M_O/M_H)=√(32/2)=4:1.