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
A steel rod $100\, cm$ long is damped at into middle. The fundamental frequency of longitudinal vibrations of the rod are given to be $2.53\, kHz$. What is the speed of sound in sound is steel ? (in $km/s$)
A string in musical instrument is $50 cm$ long and its fundamental frequency is $800 Hz.$ If a frequency of $1000 Hz$ is to be produced, then required length of string is ..... $cm$
A steel rod $100 \,cm$ long is clamped at its middle. The fundamental frequency of longitudinal vibrations of the rod are given to be $2.53\,kHz$. What is the speed of sound in steel ..... $km/sec$
Unlike a laboratory sonometer, a stringed instrument is seldom plucked in the middle. Supposing a sitar string is plucked at about $\frac{1}{4}$th of its length from the end. The most prominent harmonic would be
The total length of a sonometer wire between fixed ends is $110\, cm$. Two bridges are placed to divide the length of wire in ratio $6 : 3 : 2$. The tension in the wire is $400\, N$ and the mass per unit length is $0.01\, kg/m$ . What is the minimum common frequency with Which three parts can vibrate ........... $Hz$ ?