Question

A stretched string of length $l$ , fixed at both ends, can sustain stationary waves 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

The correct option is D $\lambda =\frac{2l}{p}$

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:
$\lambda =\frac{2l}{p}$ where, $p=1,2,\mathrm{3..}$