Question

A stretched string of length $l$, fixed at both ends, can sustain Stationary waves of wavelength of wavelength $\lambda,$ correctly given by

• A. $\lambda=\frac{l^2}{2p}$
• B. $\lambda=\frac{p^2}{2l}$
• C. $\lambda=2lp$
• D. $\lambda=\frac{2l}{p}$

Answer 1

Answer: (D)

If the string has a length $l$ and both ends are fixed then only vibrational modes are allowed where an integer number of half-wavelengths equals the string length. Now the fundamental wavelength in the wire is:
$\lambda=\frac{2 l }{ p }$ where, $p =1,2,3 . .$