At the poles, a stretched wire of a given length vibrates in unison with a tuning fork. At the equator, for same setting to produce resonance with same fork, the vibrating length of wire

A uniform metal wire has length $L$, mass $M$ and density $\rho$. It is under tension $T$ and $v$ is the speed of transverse wave along the wire. The area of cross-section of the wire is

The fundamental frequency of a closed pipe is 400 Hz . If $\frac{1}{3}$ rd pipe is filled with water, then the frequency of 2nd harmonic of the pipe will be (neglect and correction)

A sonometer wire under suitable tension having specific gravity $$\rho$$, vibrates with frequency $$n$$ in air. If the load is completely immersed in water the frequency of vibration of wire will become