The tension in a piano wire is $10N$. What should be the tension in the wire to produce a note of double the frequency .... $N$

Two uniform strings of mass per unit length $\mu$ and $4 \mu$, and length $L$ and $2 L$, respectively, are joined at point $O$, and tied at two fixed ends $P$ and $Q$, as shown in the figure. The strings are under a uniform tension $T$. If we define the frequency $v_0=\frac{1}{2 L} \sqrt{\frac{T}{\mu}}$, which of the following statement($s$) is(are) correct?

$(A)$ With a node at $O$, the minimum frequency of vibration of the composite string is $v_0$

$(B)$ With an antinode at $O$, the minimum frequency of vibration of the composite string is $2 v_0$

$(C)$ When the composite string vibrates at the minimum frequency with a node at $O$, it has $6$ nodes, including the end nodes

$(D)$ No vibrational mode with an antinode at $O$ is possible for the composite string

Which order of harmonics is missing or absent in case of stationary sound waves produced in a closed pipe ?

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 $0\,^oC = 332\,m/s]$

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 ..... $\%$

Standing waves are produced in $10 \,m$ long stretched string fixed at both ends. If the string vibrates in $5$ segments and wave velocity is $20 \,m / s$, the frequency is ....... $Hz$