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, $y(x,~t)=0.005 ~\sin(80.0x-3.0t),$ 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 $\gamma=7/5 \text)$
1. $240 ~\text{m/s}$ 
2. $331.5~\text{m/s}$ 
3. $384.5~\text{m/s}$ 
4. $280~\text{m/s}$ 

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.

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