The correct option is C Pressure nodes are located at 7.5 cm,15 cm,22.5 cm from the end.
Given that,
Δp=8sin(2πx15)cos(48πt) .........(1)
The equation of standing wave in an open organ pipe is given by
Δp=2Δpmsin(kx)cos(ωt) .........(2)
Comparing equation (1) and (2),
Excess pressure Δp(x)=8sin(2πx15)
At x=52 m,
Δp(x)=8sin(2π15×52)
⇒Δp(x)=8sin(π3)=8×√32=4√3 N/m2
and k=2πλ=2π15⇒λ2=7.5 cm
Pressure nodes will be located at x=nλ2 where n=0,1,2,3....
So, pressure nodes are
For n=0 , x=0 cm
n=1 , x=7.5 cm
n=2 , x=15 cm
n=3 , x=22.5 cm
Hence, options (a) and (c) are the correct answers.