$A$ wire of length $L$ and linear density $m$ is stretched between two rigid supports with tension $T$. It is observed that the wire resonates in the $P^{th}$ harmonic at a frequency of $320 \ Hz$ and resonates again at the next higher frequency of $400 \ Hz$. The value of $p$ is:

$L$ length and $M$ mass uniform wire is stretched between two fixed points with tension $F$. $A$ sound of frequency $\mu$ is impressed on it. The maximum vibrational energy exists in the wire when $\mu$ =

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 .... $\%$

The equation of vibration of a stretched string fixed at both ends and vibrating in $5^{\text{th}}$ harmonic is $Y = 3 \sin(0.4x) \cos(200\pi t)$, where '$x$' and '$Y$' are in $cm$ and '$t$' is in seconds. The length of the string is: (in $\pi \text{ cm}$)

One insulated conductor from a household extension cord has a mass per unit length of $\mu$. $A$ section of this conductor is held under tension between two clamps. $A$ subsection is located in a magnetic field of magnitude $B$ directed perpendicular to the length of the cord. When the cord carries an $AC$ current of $i$ at a frequency of $f$,it vibrates in resonance in its simplest standing-wave vibration state. Determine the relationship that must be satisfied between the separation $d$ of the clamps and the tension $T$ in the cord.

$A$ wire under tension vibrates with a fundamental frequency of $600 \,Hz$. If the length of the wire is doubled, the radius is halved and the wire is made to vibrate under one-ninth the tension. Then the fundamental frequency will become (in $\,Hz$)