Which one of the following statements is true?

1.	Both light and sound waves in the air are transverse.
2.	The sound waves in the air are longitudinal while the light waves are transverse.
3.	Both light and sound waves in the air are longitudinal.
4.	Both light and sound waves can travel in a vacuum.

A tuning fork of frequency \(512~\text{Hz}\) makes \(4~\text{beats/s}\) with the vibrating string of a piano. The beat frequency decreases to \(2~\text{beats/s}\) when the tension in the piano string is slightly increased. The frequency of the piano string before increasing the tension was:
1. \(510~\text{Hz}\) 
2. \(514~\text{Hz}\) 
3. \(516~\text{Hz}\) 
4. \(508~\text{Hz}\) 

\(4.0~\text{gm}\) of gas occupies \(22.4~\text{litres}\) at NTP. The specific heat capacity of the gas at a constant volume is  \(5.0~\text{JK}^{-1}\text{mol}^{-1}.\) If the speed of sound in the gas at NTP is \(952~\text{ms}^{-1},\) then the molar heat capacity at constant pressure will be:
(\(R=8.31~\text{JK}^{-1}\text{mol}^{-1}\)) 

A wave travelling along a string is described by, \(y(x,~t)=0.005 ~\sin(80.0x-3.0t),\) in which the numerical constants are in SI units. The displacement \(y\) of the wave at a distance \(x = 30.0~\text {cm}\) and time \(t=20~\text{s}\) is:
1. \(0.5~\text{mm}\)
2. \(5~\text{mm}\)
3. \(5~\text{m}\)
4. \(5~\text{cm}\)

A steel wire \(0.72~\text{m}\) long has a mass of \(5\times10^{-3}~\text{kg}\). If the wire is under tension of \(60~\text{N}\), the speed of transverse waves on the wire will be:
1. \(85~\text{m/s}\)
2. \(83~\text{m/s}\)
3. \(93~\text{m/s}\)
4. \(100~\text{m/s}\)

The speed of sound in air at standard temperature and pressure is:
(Given the mass of \(1\) mole of air is \(29.0\times10^{-3}~\text{kg}\) and $\mathrm{}$\(\gamma=7/5 \text)\)
1. \(240 ~\text{m/s}\) 
2. \(331.5~\text{m/s}\) 
3. \(384.5~\text{m/s}\) 
4. \(280~\text{m/s}\) 

Which of the following is a mechanical wave?
1. Radio waves
2. \(X\text-\)rays
3. Light waves
4. Sound waves

Two strings \(A\) and \(B,\) made of the same material, are stretched by the same tension. The radius of string \(A\) is double of the radius of \(B.\) A transverse wave that travels on \(A\) with a speed \(v_A\) and on \(B\) with a speed \(v_B.\) The ratio of  \(\frac{v_A}{v_B}\) is: