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 ?
All the points on the string between two consecutive nodes vibrate with same frequency, phase and amplitude.
All the points on the string between two consecutive nodes vibrate with same frequency and phase but different amplitude
All the points on the string between two consecutive nodes vibrate with different frequency and phase but same amplitude
All the points on the string between twoconsecutive nodes vibrate with different frequency, phase and amplitude
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 $= 340 \,m/s$)