Question

The length of a sonometer wire is $90cm$ and the stationary wave setup in the wire is represented by an equation $y=6sin\left(\frac{\pi x}{30}\right)cos\left(250t\right)$ where $x,y$ are in $cm$ and $t$ is in $sec$. The number of loops formed in the sonometer wire is

• A. $2$
• B. $1$
• C. $4$
• D. $3$

Answer 1

The correct option is D $3$

Wave length in the fundamental mode is $\lambda =2l=2\times 90cm=180cm$

Observed wavelength from the given equation is ${\lambda }^{\prime }=\frac{2\pi }{K}$

${\lambda }^{\prime }=\frac{2\pi }{\left(\frac{\pi }{30}\right)}=60cm$

Wave length in $p^{th}$ mode is ${\lambda }^{\prime }=\frac{2l}{P}$
Here number of loops is $P$

$\therefore$ No. of loops $P=\frac{2l}{{\lambda }^{\prime }}=\frac{180}{60}=3$