A stretched string is fixed at both ends. It is made to vibrate so that the total number of nodes formed in it is ' $x$ '. The length of the string in terms of the wavelength of waves formed in it is ( $\lambda=$ wavelength $)$

A sonometer wire is stretched by hanging a metal bob. The fundamental frequency of vibration of wire is ' $n_1$ '. When the bob is completely immersed in water, the frequency of vibration of wire becomes ' $n_2$ '. The relative density of the metal of the bob is

Two simple harmonic progressive waves have displacements $\rightarrow \mathrm{y}_1=\mathrm{a}_1 \sin \left(\frac{2 \pi \mathrm{x}}{\lambda}-\omega \mathrm{t}\right)$ and $\mathrm{y}_2=\mathrm{a}_2 \cos \left(\frac{2 \pi \mathrm{x}}{\lambda}-\omega \mathrm{t}+\phi\right)$ What is the phase difference between two waves?

A wire under tension 225 N produces 6 beats per second when it is tuned with a fork. When the tension changes to 256 N , it is again tuned with the same tuning fork, the number of beats remain unchanged. The frequency of tuning fork will be