v_(N2)/v_He =√(γ_(N2)/γ_He ×M_He/M_(N2))=√((7/5)/(5/3)×4/28)=√3/5.

According to Hooke’s law,
Tension (T) is proportional to Extension (x)
Also, speed of sound,
v∝√T
v^‘∝√1.5x
v^‘/v=√1.5=1.22
v^‘=1.22v.

y=Asin(kx-ωt)
u=dy/dt=-ωAcos(kx-ωt)
u_max=ωA.

For the formation of a stationary wave, two identical waves travelling in opposite directions must separate each other. At x=0, resultant y should be zero for getting a node. Hence -acos(kx+ωt) is the correct answer.

v^‘=v/(v-v_s)×v
v^‘=330/(330-33)×450=500Hz.