EXERCISE

A copper wire is held at the two ends by rigid supports. At $30{ }^{\circ }\mathrm{C}$, the wire is just taut, with negligible tension. Find the speed(in $\mathrm{m} {\mathrm{s}}^{-1}$) of transverse waves in this wire at $10{ }^{\circ }\mathrm{C}$ to the nearest integer.

($Y$ for copper = $1.3\times {10}^{11} \mathrm{N} {\mathrm{m}}^{-2}$; $\alpha =1.7 \times {10}^{-5}{ }^{\mathrm{o}}{\mathrm{C}}^{-1}$ and density = $9\times {10}^3 \mathrm{kg} {\mathrm{m}}^{-3}$)

A wire of density $9 g/ c{m}^3$ is stretched between two clamps 100 cm apart while subjected to an extension of 0.05 cm. What is the lowest frequency of transverse vibration in the wire?

Young's modulus of the material is $9\times {10}^{11} dyne c{m}^{-2}$

Three wires A, B and C of same lengths are stretched by a weight. Their relative masses are $2:8:18$ and tensions in them are $12:12:27$. The ratio of their fundamental frequencies is $x:1:1$. Find the value of $x$.

A length of wire vibrates in unison with a fork of frequency $320 \mathrm{Hz}$ when the tension is $3 kg wt$. If the wire is replaced by one of the same material but twice the diameter, what tension would their be required so that the same length is in unison with a fork of frequency $256 \mathrm{Hz}$?

(Answer nearest to two decimal places)

Two wires are fixed on a sonometer. The tensions are in the ratio $8:1$, the lengths in ratio $36:35$, the diameters in the ratio $4:1$ and the densities are in the ratio $1:2$. Find the frequency of beats produced if the note of the higher pitch has a frequency of 360 per second.

The length of the wire between the pulleys is $1.5$ metre and its mass is $12 \mathrm{g}$. Two weights, each of $9 \mathrm{kg}$, are suspended from the pulleys. Find the frequency(to the nearest integer in Hz) of transverse vibrations of the string when the string vibrates in two loops with the middle point of the wire between the pulleys at rest.

($g=10 \mathrm{m} {\mathrm{s}}^{-2}$)

A certain organ pipe resonates in its fundamental mode at a frequency of 500 Hz in air. What will be the fundamental frequency if the air is replaced by hydrogen at the same temperatures? Density of air is $1.20 kg m^{-3}$ and that of hydrogen is $0.089 kg m^{-3}$.

A swimmer sends a sound signal from the bottom of a lake to the surface 0.5 beats will be heard if the signal is compared with the fundamental tone of a closed pipe of length 20cm. What is the wavelength of sound in water? Velocity of sound in air =360 m/s and in water = 1500 m/s.