A wire having a linear mass density $9.0 \times 10^{-4} \;{kg} / {m}$ is stretched between two rigid supports with a tension of $900\; {N}$. The wire resonates at a frequency of $500\;{Hz}$. The next higher frequency at which the same wire resonates is $550\; {Hz}$. The length of the wire is $...... {m}$

The given diagram shows three light pieces of paper placed on a wire that is stretched over two supports, $Q$ and $R$ , a distance $4x$ apart. When the wire is made to vibrate at a particular frequency, all the pieces of paper, except the middle one, fall off the wire. Which of the following could be the wavelength of the vibration?

Two uniform strings $A$ and $B$ made of steel are made to vibrate under the same tension. if the first overtone of $ A$ is equal to the second overtone of $B$ and if the radius of $A$ is twice that of $B,$ the ratio of the lengths of the strings is

Figure, shows a stationary wave between two fixed points $P$ and $Q$. Which point$(s)$ of $1, 2$ and $3$ are in phase with the point $X?$

When a wave travelling in medium is reflected from the boundary of a denser medium, which of the following will not change?

A tuning fork of frequency $280\,\, Hz$ produces $10$ beats per sec when sounded with a vibrating sonometer string. When the tension in the string increases slightly, it produces $11$ beats per sec. The original frequency of the vibrating sonometer string is ... $Hz$