Physics - Wave on String Question with Solution | TestHub

Trough to crest distance

$1.5=\left(2{\mathrm{n}}_1+1\right)\frac{\mathrm{\lambda }}{2}$           ......$\left(1\right)$

Trough to trough distance

$5=\left({\mathrm{n}}_2\mathrm{\lambda }\right)$         .....$\left(2\right)$

from $\left(1\right)$ and $\left(2\right)$

$\frac{1.5}{5}=\frac{2{\mathrm{n}}_1+1}{2\left({\mathrm{n}}_2\right)}$

$3{\mathrm{n}}_2=10{\mathrm{n}}_1+5$

${\mathrm{n}}_1$ and ${\mathrm{n}}_2$ are integer

$\left(1\right)$ ${\mathrm{n}}_1=1,{\mathrm{n}}_2=5,\mathrm{\lambda }=1$

$\left(2\right)$ ${\mathrm{n}}_1=4,{\mathrm{n}}_2=15,\mathrm{\lambda }=1/3$

$\left(3\right)$ ${\mathrm{n}}_1=7,{\mathrm{n}}_2=25,\mathrm{\lambda }=1/5$