The equation \(y(x,t) = 0.005 ~cos (\alpha x- \beta t)\) describes a wave traveling along the x-axis. If the wavelength and the time period of the wave are 0.08 m and 2.0 s, respectively, then $\mathrm{\alpha }$ and $\mathrm{\beta }$ in appropriate units are:

1. $\mathrm{\alpha }=25.00$ $\mathrm{\pi },$ $\mathrm{\beta }=\mathrm{\pi }$

2. $\mathrm{\alpha }=\frac{0.08}{\mathrm{\pi }},$ $\mathrm{\beta }=\frac{2.0}{\mathrm{\pi }}$

3. $\mathrm{\alpha }=\frac{0.04}{\mathrm{\pi }},$ $\mathrm{\beta }=\frac{1.0}{\mathrm{\pi }}$

4. $\mathrm{\alpha }=12.50$ $\mathrm{\pi },$ $\mathrm{\beta }=\frac{\mathrm{\pi }}{2.0}$

A vibrating tuning fork of frequency n is placed near the open end of a long cylindrical tube.           
           
The tube has a side opening and is also fitted with a movable reflecting piston. As the piston is moved through 8.75 cm, the intensity of sound changes from a maximum to a minimum. If the speed of sound is 350 metre per second, then n is -

1.  500 Hz
2.  1000 Hz
3.  2000 Hz
4.  4000 Hz

In an experiment with a sonometer, a tuning fork of frequency 256 Hz resonates with a length of 25 cm and another tuning fork resonates with a length of 16 cm. If the tension of the string remains constant, then the frequency of the second tuning fork will be:

1. 163.84 Hz

2. 400 Hz

3. 320 Hz

4. 204.8 Hz

The rate of energy transfer in a wave depends:

Two identical wires are stretched by the same tension of 100 N and each emits a note of 200 Hz. If tension in one wire is increased by 1 N, the number of beats heard per second when the wires are plucked will be:

A tuning fork with a frequency of \(800\) Hz produces resonance in a resonance column tube with the upper end open and the lower end closed by the water surface. Successive resonances are observed at lengths of \(9.75\) cm, \(31.25\) cm, and \(52.75\) cm. The speed of the sound in the air is:

Two waves represented by the following equations are travelling in the same medium \(y_1 = 5 sin2\pi (75t-0.25x)\), \(y_2 = 10 sin2\pi (150t-0.50x)\)${\mathrm{}}_{}$
The intensity ratio \(\frac{I_1}{I_2}\) of the two waves will be:
1. \(1:2\)
2. \(1:4\)
3. \(1:8\)
4. \(1:16\)

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:

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: