Question 348: Waves

Question

A stretched string is fixed at both ends. It is made to vibrate so that the total number of nodes formed in it is ' $x$ '. The length of the string in terms of the wavelength of waves formed in it is ( $\lambda=$ wavelength $)$

Accepted Answer

For a string fixed at both ends, when it vibrates in a standing wave pattern, nodes are points where there is no movement. The distance between two consecutive nodes is equal to half the wavelength, $\frac{\lambda}{2}$.
If the total number of nodes formed is $x$, then these nodes divide the string into $x-1$ segments where each segment is half the wavelength long. Therefore, the length of the string $L$ can be determined by the following relationship:
$ L = (x-1) \cdot \frac{\lambda}{2}  $
Thus, the correct expression for the length of the string in terms of the wavelength $\lambda$ and the number of nodes $x$ is:
Option D:
$ L = (x-1) \frac{\lambda}{2} $

Answer

$\frac{\mathrm{X} \lambda}{2}$

Answer

$\left(\mathrm{X}+\frac{1}{2}\right) \frac{\lambda}{2}$

Answer

$(\mathrm{X}+1) \frac{\lambda}{2}$

Answer

$(\mathrm{X}-1) \frac{\lambda}{2}$

Waves

A stretched string is fixed at both ends. It is made to vibrate so that the total number of nodes formed in it is ' x '. The length of the string in terms of the wavelength of waves formed in it is ( \lambda= wavelength )

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