The transverse displacement of a string clamped at its both ends is given by 

$y\left( {x,t} \right) = 2\,\sin \,\left( {\frac{{2\pi }}{3}x} \right)\,\cos \,\left( {100\,\pi t} \right)$ 

where $x$ and $y$ are in $cm$ and $t$ is in $s$. Which of the following statements is correct ?

  • A

    All the points on the string between two consecutive nodes vibrate with same frequency, phase and amplitude.

  • B

    All the points on the string between two consecutive nodes vibrate with same frequency and phase but different amplitude

  • C

    All the points on the string between two consecutive nodes vibrate with different frequency and phase but same amplitude

  • D

    All the points on the string between twoconsecutive nodes vibrate with different frequency, phase and amplitude

Similar Questions

When an air column at $15\,^oC$ and a tunning fork are sounded together then $4$ beats per second are produced, the frequency of the fork is less then that of air column. When the temperature falls to $10\,^oC$ , then the beat frequency decreases by one. The frequency of the fork will be ..... $Hz$ $[V_{sound}$ at $0\,^oC = 332\,m/s]$

A string is producing transverse vibration whose equation is $y = 0.021\;\sin (x + 30t)$, Where $x$ and $y$ are in meters and $t$ is in seconds. If the linear density of the string is $1.3 \times {10^{ - 4}}\,kg/m,$ then the tension in the string in $N$ will be

A transverse harmonic wave on a string is described by $y = 3 \sin \,(36t + 0.018x + \frac{\pi}{4})$ where $x$ and $y$ are in $cm$ and $t$ in $s$. The least distance between  two sucessive crests in the wave is .... $m$

The given diagram shows three light pieces of paper placed on a wire that is stretched over two supports, $Q$ and $R$ , a distance $4x$ apart. When the wire is made to vibrate at a particular frequency, all the pieces of paper, except the middle one, fall off the wire. Which of the following could be the wavelength of the vibration?

A tuning fork of frequency $340\, Hz$ is sounded above an organ pipe of length $120\, cm$. Water is now slowly poured in it. The minimum height of water column required for resonance is .... $cm$ (speed of sound in air $= 340 \,m/s$)