Question

A stretched string of length L, fixed at both ends can sustain stationary waves of wavelength $\lambda $ . Which of the following value of wavelength is not possible?

• A. $2L$
• B. $4L$
• C. $L$
• D. $\frac{L}{2}$

Answer 1

Answer: (B)

The general equation for $nth$ harmonics in terms of length and wavelength is, $L=\frac{n}{2}\lambda ,n\in N$
Following the above expression the possible values of wavelength for harmonics are,
$\lambda =2L\Rightarrow n=1\lambda =L\Rightarrow n=2\lambda =\frac{L}{2}\Rightarrow n=4\lambda =4L\Rightarrow n=\frac{1}{2},but\frac{1}{2}\notin N$
Therefore, $\lambda =4L$ is not possible.