A transverse harmonic wave on a string is described by $y = 3\sin \left( {36t + 0.018x + \frac{\pi }{4}} \right)$ where $x$ and $y$ are in $cm$ and $t$ in $s$. The least distance between two successive crests in the wave is .... $m$
$2.5$
$3.5$
$1.5$
$4.5$
When two waves of almost equal frequencies $v_1$ and $v_2$ reach at a point simultaneously, the time interval between successive maxima is
Beats are produced by two waves $y_1 = a\, sin\, (1000\, \pi t)$ and $y^2 = a\, sin\, (998\, \pi t)$ The number of beats heard per second is
A massless rod is suspended by two identical strings $AB$ and $CD$ of equal length. A block of mass $m$ is suspended from point $ O $ such that $BO$ is equal to $’x’$. Further, it is observed that the frequency of $1^{st}$ harmonic (fundamental frequency) in $AB$ is equal to $2^{nd}$ harmonic frequency in $CD$. Then, length of $BO$ is
Two trains $A$ and $B$ initially $120\, km$ apart, start moving towards each other on the same track with a velocity of $60\, km/hr$ each. At the moment of start $A$ blows a whistle, which reflects on $B$ and subsequently reflects from $A$ and so on. Take the velocity of sound waves in air $1200\, km/hr$. The distance travelled by sound waves before the trains crash will be (in $km$)
When a string is divided into three segments of length $l_1,\,l_2$ and $l_3,$ the fundamental frequencies of these three segments are $v_1,\,v_2$ and $v_3$ respectively. The original fundamental frequency $(v)$ of the string is