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

  • A

    $x/\sqrt 2 $

  • B

    $\sqrt 2 x$

  • C

    $x/2$

  • D

    $2x$

Similar Questions

The equation of a wave on a string of linear mass density $0.04\, kgm^{-1}$ is given by : $y = 0.02\,\left( m \right)\,\sin \,\left[ {2\pi \left( {\frac{t}{{0.04\left( s \right)}} - \frac{x}{{0.50\left( m \right)}}} \right)} \right]$. The tension in the string is ..... $N$

One insulated conductor from a household extension cord has a mass per unit length of $μ.$ A section of this conductor is held under tension between two clamps. A subsection is located in a magnetic field of magnitude $B$ directed perpendicular to the  length of the cord. When the cord carries an $AC$ current of $"i"$ at a frequency of $f,$ it  vibrates in resonance in its simplest standing-wave vibration state. Determine the  relationship that must be satisfied between the separation $d$ of the clamps and the tension $T$ in the cord.

A transverse wave is passing through a string shown in figure. Mass density of the string is $1 \ kg/m^3$ and cross section area of string is $0.01\ m^2.$ Equation of wave in string is $y = 2sin (20t - 10x).$ The hanging mass is (in $kg$):-

The speed of a transverse wave passing through a string of length $50 \;cm$ and mass $10\,g$ is $60\,ms ^{-1}$. The area of cross-section of the wire is $2.0\,mm ^{2}$ and its Young's modulus is $1.2 \times 10^{11}\,Nm ^{-2}$. The extension of the wire over its natural length due to its tension will be $x \times 10^{-5}\; m$. The value of $x$ is $...$

  • [JEE MAIN 2022]

A $20 \mathrm{~cm}$ long string, having a mass of $1.0 \mathrm{~g}$, is fixed at both the ends. The tension in the string is $0.5 \mathrm{~N}$. The string is set into vibrations using an external vibrator of frequency $100 \mathrm{~Hz}$. Find the separation (in $cm$) between the successive nodes on the string.

  • [IIT 2009]