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A sonometer wire of length $1.5 \mathrm{m}$ is made of steel. The tension in it produces an elastic strain of $1\%.$ What is the fundamental frequency of steel, if density and elasticity of steel are $7.7\times {10}^3 \mathrm{kg}/{\mathrm{m}}^3 \mathrm{and} 2.2\times {10}^{11} \mathrm{N}/{\mathrm{m}}^2$ respectively? 

A pipe of:length $85 \mathrm{cm}$is closed from one end. Find the number of possible natural oscillations of air column in the pipe whose frequencies lie below $1250 \mathrm{Hz}$. The velocity of sound in air is $340 \mathrm{m} {\mathrm{s}}^{-1}$.

A pipe open at both ends has a fundamental frequency $f$ in air. The pipe is dipped vertically in water so that half of it is in water. The fundamental frequency of the air column is now

A hollow pipe of length $0.8 \mathrm{m}$ is closed at one end. At its open end, a $0.5 \mathrm{m}$ long uniform string is vibrating in its second harmonic and it resonates with the fundamental frequency of the pipe. If the tension in the wire is $50 \mathrm{N}$ and the speed of sound is $320 \mathrm{m} {\mathrm{s}}^{-1}$, the mass of the string is

A student is performing the experiment of Resonance Column. The diameter of the column tube is $4 \mathrm{cm}$. The frequency of the tuning fork is $512 \mathrm{Hz}$ The air temperature is $38°\mathrm{C}$ in which the speed of sound is $336 \mathrm{m}/\mathrm{s}$  The zero of the meter scale coincides with the top of the resonance column tube. When the first resonance occurs, the reading of the water level in the column is

A student is performing an experiment using a resonance column and a tuning fork of frequency $244 {\mathrm{s}}^{-1}$. He told that the air in the tube has been replaced by another gas (assume that the column remains filled with the gas). If the minimum height at which resonance occurs is $\left(0.350\pm 0.005\right) \mathrm{m}$, the gas in the tube is (useful information: $\sqrt{167RT}=640 {\mathrm{J}}^{\frac{1}{2}} \mathrm{mole}{ }^{-\frac{1}{2}}, \sqrt{140RT}=590 {\mathrm{J}}^{\frac{1}{2}} \mathrm{mole}{ }^{-\frac{1}{2}}$. The molar mass $M$ in grams and given in the options. Take the values of $\sqrt{\frac{10}{M}}$ for each gas as given there). 

One end of taut string of length $3\mathrm{m}$ along the X-axis is fixed at $x=0$. The speed of the wave in the string is $100 \mathrm{m}/\mathrm{s}$. The other end of the string is vibrating in the Y direction so that stationary waves are set up in the string. The possible waveform (s) of these stationary waves is (are)

A $20 \mathrm{cm}$ long string, having a mass of $1.0 \mathrm{g},$ is fixed at both the ends. The tension in the string is $0.5 \mathrm{N}.$ The string is set into vibrations using an external vibrator of frequency $100 \mathrm{Hz}.$ Find the separation (in $\mathrm{cm}$ ) between the successive nodes on the string.