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:

1.	\(500\) m/s	2.	\(156\) m/s
3.	\(344\) m/s	4.	\(172\) m/s

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. \(1:16\)

The rate of energy transfer in a wave depends:

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

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

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

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 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?

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: