A wave travelling along a string is described by, \(y(x,t)=0.005 \text{sin}(80.0x-3.0t),\) in which the numerical constants are in SI units. The wavelength and the period of the wave respectively are: 
1. \(7.85\) cm and \(2.09\) s
2. \(7.85\) mm and \(1.09\) s
3. \(7.85\) m and \(0.09\) s
4. none of these

A wave travelling along a string is described by, \(y(x,~t)=0.005 \mathrm{sin}(80.0x-3.0t),\) in which the numerical constants are in SI units. The displacement \(y\) of the wave at a distance \(x = 30.0\) cm and time \(t=20\) s is:
1. \(0.5\) mm
2. \(5\) mm
3. \(5\) m
4. \(5\) 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. \(100~\text{m/s}\)

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

Two sitar strings A and B playing the note ‘Dha’ are slightly out of tune and produce beats of frequency \(5\) Hz. The tension of the string B is slightly increased and the beat frequency is found to decrease to \(3\) Hz. What is the original frequency of B if the frequency of A is \(427\) Hz?
1. \(432\) Hz
2. \(424\) Hz
3. \(430\) Hz
4. \(422\) Hz

A pipe, 30.0 cm long, is open at both ends.

(i) Which harmonic mode of the pipe resonates a 1.1 kHz source?

(ii) Will resonance with the same source be observed if one end of the pipe is closed?

Take the speed of sound in air as 330 m s^–1.