A string is stretched between two fixed points separated by $75 \mathrm{cm}.$ It is observed to have resonant frequencies of $420 \mathrm{Hz} \mathrm{and} 315 \mathrm{Hz}.$ There are no other resonant frequencies between these two. Then, the lowest resonant frequency for this string is :

The linear density of a vibrating string is $1.3\times {10}^{-1} \mathrm{kg} {\mathrm{m}}^{-1}.$ In this string, a transverse wave is propagating whose equation is $\mathrm{y}=0.021 \sin \left(\mathrm{x}+30\mathrm{t}\right),$ where $\mathrm{x} \mathrm{and} \mathrm{y}$ are measured in meter and $\mathrm{t}$ in second. The approximate tension in the string is :

What type of vibration are produced in a sonometer wire?

The transverse displacement $\mathrm{y}\left(\mathrm{x},\mathrm{t}\right)$ of a wave on a string is given by $\mathrm{y}\left(\mathrm{x},\mathrm{t}\right)={\mathrm{e}}^{-\left({\mathrm{ax}}^2+{\mathrm{bt}}^2+2\sqrt{\mathrm{ab}}\mathrm{xt}\right)}.$ This represents a:

A tuning-fork vibrating with a sonometer wire of length $20 \mathrm{cm}$ produces $5$ beats per second. The beat frequency does not change if the length of the wire is changed to $21 \mathrm{cm}.$ The frequency of the tuning-fork (in hertz) must be :

A tuning fork of frequency $480 \mathrm{hertz}$ vibrating with a sonometer wire produces $10 \mathrm{beats} \mathrm{per} \sec .$ If on lightening the wire the number of beats per second decreases, then the frequency of the wire will be :

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

A horizontal stretched string fixed at two ends, is vibrating in its fifth harmonic according to the equation $\mathrm{y}\left(\mathrm{x},\mathrm{t}\right)=0.01 \mathrm{m} \sin \left[\left(62.8 {\mathrm{m}}^{-1}\right)\mathrm{x}\right] \cos \left[\left(628 {\mathrm{s}}^{-1}\right)\mathrm{t}\right].$ Assuming $\mathrm{\pi }=3.14,$ the correct statement is (are)