A stretched wire of length $110\,cm$ is divided into three segments whose frequencies are in ratio $1 : 2 : 3.$ Their lengths must be

When a wave travels in a medium, the particle displacement is given by : $y = asin\, 2 \pi \,(bt -cx)$, where $a, b$ and $c$ are constants. The maximum particle velocity will  be twice the wave velocity if

Two identical piano wires, kept under the same tension $T$ have a fundamental frequency of $600\, Hz$. The fractional increase in the tension of one of the wires which will lead to occurrence of $6\, beats/s$ when both the wires oscillate together would be

When two waves of almost equal frequencies $v_1$ and $v_2$ reach at a point simultaneously, the time interval between successive maxima is

Fundamental frequency of a sonometer wire is $n$. If the length and diameter of the wire are doubled keeping the tension same, then the new fundamental frequency is

A point source emits sound equally in all directions in a non-absorbing medium. Two points $P$ and $Q$ are at a distance of $9$ meters and $25$ meters respectively from the source. The ratio of the amplitudes of the waves at $P$ and $Q$ is