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 wire of length $2\,L$ is made by joining two wires $A$ and $B$ of same lengths but different radii $r$ and $2r$ and made of the same material. It is vibrating at a frequency such that the joint of the two wires forms a node. If the number of antinodes in wire $A$ is $p$ and that in $B$ is $q$ then the ratio $p : q$ is

In an experiment with sonometer a tuning fork of frequency $256 Hz$ resonates with a length of $25 cm$ and another tuning fork resonates with a length of $16 cm$. Tension of the string remaining constant the frequency of the second tuning fork is ....  $Hz$

A string $1\,\,m$ long is drawn by a $300\,\,Hz$ vibrator attached to its end. The string vibrates in $3$ segments. The speed of transverse waves in the string is equal to .... $m/s$

A wave on a string is travelling and the displacement of particles on it is given by $x = A\, sin\, (2t -0.1\, x)$. Then the wavelength of the wave is

A wire having a linear mass density $9.0 \times 10^{-4} \;{kg} / {m}$ is stretched between two rigid supports with a tension of $900\; {N}$. The wire resonates at a frequency of $500\;{Hz}$. The next higher frequency at which the same wire resonates is $550\; {Hz}$. The length of the wire is $...... {m}$