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

When an air column at $15\,^oC$ and a tunning fork are sounded together then $4$ beats per second are produced, the frequency of the fork is less then that of air column. When the temperature falls to $10\,^oC$ , then the beat frequency decreases by one. The frequency of the fork will be ..... $Hz$ $[V_{sound}$ at $0\,^oC = 332\,m/s]$

A transverse wave is passing through a stretched string with a speed of $20\  m/s.$ The tension in the string is $20\  N$. At a certain point $P$ on the string, it is observed that energy is being transferred at a rate of $40 \ mW$ at a given instant. Find the speed of point $P$.

The string of a violin has a frequency of $440 \,cps$. If the violin string is shortened by one fifth, its frequency will be changed to ........... $cps$

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 .... $\%$

The tension of a stretched string is increased by $69\%$. In order to keep its frequency of vibration constant, its length must be increased by .... $\%$