A standing wave is represented by $Y=A\sin \left(100t\right)\cos (0.01x)$ where Y and A are in millimetres, t is in seconds and x is in metres. The velocity of the wave is:

1.	104 m/s
2.	1 m/s
3.	10–4 m/s
4.	Not derivable from the above data

Two progressive waves are represented by, \(y_1=5sin(200t-3.14x)\) and
 \(y_2=10sin(200t-3.14x+\frac{\pi}{3})\) (\(x\) is in metres, and \(t\) is in seconds). Path difference between the two waves is:
1. $\frac{100}{\mathrm{\pi }}\mathrm{ m}$

2. $\frac{1}{3}\mathrm{ m}$

3. $3.14\times \frac{\mathrm{\pi }}{3}\mathrm{ m}$

4. $\frac{{\mathrm{\pi }}^2}{9}\mathrm{ m}$

Two organ pipes closed at one end produce 5 beats per second in fundamental mode. If the ratio of their lengths is 10:11, then their frequencies (in Hz) are:

If a travelling wave pulse is given by \(y=\frac{20}{4+(x+4 t)^2}~\text{m}\), then:

Two wires, A and B, of a musical instrument 'Sitar' produce 3 beats per second. If the tension of B is raised, the number of beats becomes 1 beat per second. If the frequency of A is 450 Hz, then the original frequency of B will be:

1. 447 Hz

2. 453 Hz

3. 449 Hz

4. 451 Hz
 

A cylindrical tube open at both ends has a fundamental frequency f₀ in the air. The tube is dipped vertically in water such that half its length is inside water. The fundamental frequency of the air column now will be:

1. $\frac{3f_{\mathit{0}}}{4}$

2. $f_0$

3. $\frac{f_{\mathit{0}}}{2}$

4. 2$f_0$

 

The maximum possible wavelength in an open organ pipe of length l is:

The equation of a stationary wave is given as $\mathrm{y}=\mathrm{A}$ $\sin$ $0.5\mathrm{\pi t}$ $\cos (0.2\mathrm{\pi x}),$ $$ where t is in seconds and x in centimetres. Which of the following is correct?

The equation of a travelling wave is given as $\mathrm{y}=A\sin (40\mathrm{\pi t}-0.2\mathrm{\pi x})$, where t is in seconds and x in metres. The minimum distance between two particles oscillating in the same phase is:

1. 10 m

2. 5 m

3. 2 m 

4. 1.5 m

Two sound waves given by the equations \(y=A\sin 122 \pi t\) and \(y=A\sin 128 \pi t\) pass through a point simultaneously. The number of beats per second is: