Question

The equation of a standing wave, produced on a string fixed at both ends, is $y=\left(0.4cm\right)sin\left[\right(0.314c{m}^{-1}\left)x\right]cos\left[\right(600\pi s^{-1}\left)t\right]$

What could be the smallest length of the string?

• A. 20 cm
• B. 10 cm
• C. 15 cm
• D. None of these

Answer 1

The correct option is B

10 cm

we get from the wave equation that $\omega =600\pi$

$\Rightarrow f=\frac{\omega }{2\pi }=300Hz$

Also $k=0.314$

$\Rightarrow \frac{2\pi }{\lambda }=0.314$

$\lambda =\frac{2\pi }{0.314}$

$\lambda =20cm$

velocity,$v=f\lambda =300\times 20$

$=6000cm{s}^{-1}$

And as we know $f=\frac{nv}{2L}$

$L=\frac{nv}{2f}=\frac{n\times 6000}{2\times 300}$

$L=10n$

The least value for $n=1$

so $L_{min}=10cm$