Which one of the following graphs represents correctly the given wave equation at the origin?

$\mathrm{y}=2\sqrt{3}\sin \left(2\mathrm{\pi x}-3\mathrm{\pi t}+\frac{\mathrm{\pi }}{3}\right)$

1.		2.
3.		4.

The fundamental frequency of an open organ pipe is 200 Hz. If one end of the pipe is closed, its fundamental frequency becomes:

\(y-x\) graph of a travelling wave along \(+x\) direction is shown at any instant \(t\). (Symbols have their usual meanings). The velocity of a particle at:

Stationary waves can be obtained in an air column even if interfering waves have different:

1. Amplitude

2. Wavelength

3. Velocity

4. Frequency

A sound wave is passed through a chamber. If the r.m.s. speed of molecules in a gas is v₁ and the speed of sound is v₂ in the gas, then: 

A string of length l is fixed at one end and free at the other. If it resonates in different modes, then the ratio of frequencies is:

1. 1:2:3: ......

2. 1:3:5:7: ......

3. 1:2:4:8: ..........

4. 1:3:9: ........

Given below are two statements: 

If the transverse displacement of a string clamped at both ends is given by y(x,t)=12(cm) sin(6.28x)cos(3.14 t), where x is in cm and t is in seconds, then which of the following is not true?

Given the equation for a wave on the string, y = 0.5 sin(5x - 3t) where y and x are in metres and t in seconds, the ratio of the maximum speed of particle to the speed of wave is:

1. 1:1

2. 5:2

3. 3:2

4. 4:5

Stationary waves are formed on a stretched string. If the wavelength is $\mathrm{\lambda }$, then the distance between two points having the maximum displacement can be: