The frequency of transverse vibrations in a stretched string is $200 Hz$. If the tension is increased four times and the length is reduced to one-fourth the original value, the frequency of vibration will be  .... $Hz$

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

For a transverse wave travelling along a straight line, the distance between two peaks (crests) is $5 \,m ,$ while the distance between one crest and one trough is $1.5 \,m$ The possible wavelengths (in $m$ ) of the waves are

Two similar sonometer wires given fundamental frequencies of $500Hz$. These have same tensions. By what amount the tension be increased in one wire so that the two wires produce $5$ beats/sec .... $\%$

A steel rod $100 cm$ long is clamped at its mid-point. The funda-mental frequency of longitudinal vibrations of the rod is given to be $2.53 kHz$. What is the speed of sound in steel .... $km/s$

A pulse or a wave train travels along a stretched string and reaches the fixed end of the string. It will be reflected back with