A uniform rope of length $L$ and mass $m_{1}$ hangs vertically from a rigid support. A block of mass ${m}_{2}$ is attached to the free end of the rope. A transverse pulse of wavelength $\lambda_{1}$ is produced at the lower end of the rope. The wavelength of the pulse when it reaches the top of the rope is $\lambda_{2}$. The ratio $\frac{\lambda_{2}}{\lambda_{1}}$ is,

Two identical straight wires are stretched so as to produce $6\text{ beats per second}$ when vibrating simultaneously. On changing the tension in one of them, the beat frequency remains unchanged. Denoting by $T_1\text{,} T_2$ the higher and the lower initial tensions in the strings, it could be said that while making the above change in tension,

A string on a musical instrument is $50 \mathrm{cm}$ long and its fundamental frequency is $270 \mathrm{Hz}$. If the desired frequency of $1000 \mathrm{Hz}$ is to be produced, the required length of the string is

A string of $7 \mathrm{m}$ length has a mass of $0.035 \mathrm{kg}$. If tension in the string is $60.5 \mathrm{N}$, then speed of a wave on the string is 

A uniform string of length $L$ and mass $M$ is fixed at both ends while it is subjected to a tension $T$. It can vibrate at frequencies ( $v$ ) given by the formula (where, $n=1\text{,} 2\text{,} 3\text{...}$),

The transverse displacement of a vibrating string is, $y=0.06 \sin \frac{2 \pi}{3} x \cos (120 \pi t)$. If mass per unit length of the string is $2\times {10}^{-2} \mathrm{kg} {\mathrm{m}}^{-1}$, the tension in the string will be,

A metal wire of linear mass density $9.8 \mathrm{g} {\mathrm{m}}^{-1}$ is stretched with a tension of $10$ $\mathrm{kg}$ weight between two rigid supports $1$ $\mathrm{m}$ apart. The wire passes at its middle point between the poles of a permanent magnet and it vibrates in resonance when carrying an alternating current of frequency $n$.if $g=10 \mathrm{m} {\mathrm{s}}^{-2}$  The frequency $n$ of the alternating source is,

Standing waves are produced in a $10$ $\mathrm{m}$ long stretched string. If the string vibrates in five segments and the wave velocity is $20 \mathrm{m} {\mathrm{s}}^{-1}$, the frequency is,

In a sonometer experiment, the bridges are separated by a fixed distance. The wire which is slightly elastic emits a tone of frequency $n$ when held by tension $T$. If the tension is increased to $4T$, the tone emitted by the wire will be of frequency,