Question

The length of a Sonometer wire is 90 cm 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 seconds. The number of loops 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 $\times$ 90 cm = 180 cm

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 ${\lambda }^{\prime }=\frac{2l}{P}$

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