Spacing between two successive nodes in a sta | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) The spacing between two successive nodes in a standing wave is given by $d = \frac{\lambda}{2} = x$.From the wave equation,$V = f\lambda$,where $V

Vedclass · Accepted Answer

$\sqrt{2}x$

Vedclass · Answer

(B) The spacing between two successive nodes in a standing wave is given by $d = \frac{\lambda}{2} = x$.From the wave equation,$V = f\lambda$,where $V$ is the wave speed,$f$ is the frequency,and $\lambda$ is the wavelength.The speed of a wave on a string is $V = \sqrt{\frac{T}{\mu}}$,where $T$ is the tension and $\mu$ is the linear mass density.Since $f$ is constant,$\lambda = \frac{V}{f} \propto V \propto \sqrt{T}$.Let the initial tension be $T$ and the new tension be $T' = 2T$.The new wavelength $\lambda'$ is given by $\frac{\lambda'}{\lambda} = \sqrt{\frac{T'}{T}} = \sqrt{\frac{2T}{T}} = \sqrt{2}$.Thus,$\lambda' = \sqrt{2}\lambda$.The new spacing between nodes is $d' = \frac{\lambda'}{2} = \sqrt{2} \left( \frac{\lambda}{2} \right) = \sqrt{2}x$.

Spacing between two successive nodes in a standing wave on a string is $x$. If the frequency of the standing wave is kept unchanged but the tension in the string is doubled,then the new spacing between successive nodes will become

Similar Questions

Standing waves can be produced:

The equation of a stationary wave is given by $y = 0.8 \cos \left( \frac{\pi x}{20} \right) \sin (200 \pi t) \text{ cm}$. What is the distance between two consecutive nodes in cm?

Stationary waves can be produced in

The equation of a stationary wave along a stretched string is given by $y = 5 \sin \left( \frac{\pi x}{3} \right) \cos (40 \pi t)$. Here $x$ and $y$ are in $cm$ and $t$ is in seconds. The separation between two adjacent nodes is: (in $cm$)

$A$ wave is represented by the equation $y = 10 \sin 2\pi(100t - 0.02x) + 10 \sin 2\pi(100t + 0.02x)$. The maximum amplitude and loop length are respectively:

Vedclass Test Series

Exam Paper Generator

Online Exam Module