The path difference between two waves given by the equations

$y_1=a_1 \sin \left(\omega t-\frac{2 \pi x}{\lambda}\right)$ and $y_2=a_2 \sin \left(\omega t-\frac{2 \pi x}{\lambda}+\phi\right)$ is

If two progressive sound waves represented by $y_1=3 \sin 250 \pi t$ and $y_2=2 \sin 260 \pi t$ (where displacement is in metre and time is in second) superimpose, then the time interval between two successive maximum intensities is

In a closed organ pipe, the number of nodes formed in fifth and ninth harmonics are respectively

When a stretched wire of fundamental frequency $f$ is divided into three segments, the fundamental frequencies of these three segments are $f_1, f_2$ and $f_3$ respectively. Then the relation among $f_1, f_2, f_3$ and $f$ is (Assume tension is constant)