The equation of a standing wave in a string is \(y = (200~\text{m})\sin\left(\frac{2\pi}{50}x\right)\cos\left(\frac{2\pi}{0.01}t\right)\) where \(x\) is in metres and \(t\) is in seconds. At the position of antinode, how many times does the distance of a string particle become \(200~\text{m}\) from its mean position in one second?

1.	\(100~\text{times}\)	2.	\(50~\text{times}\)
3.	\(200~\text{times}\)	4.	\(400~\text{times}\)

In the phenomenon of interference of sound by two coherent sources if difference of intensity at maxima to intensity at minima is 20dB, then the ratio of intensities of the two sources is

1.  $\frac{121}{81}$

2.  $\frac{11}{9}$

3.  $\frac{101}{99}$

4.  $\frac{10}{1}$

If a sound source of frequency n approaches an observer with velocity v/4 and the observer approaches the source with velocity v/5, then the apparent frequency heard will be-

1.  (5/8)n

2.  (8/5)n

3.  (7/5)n

4.  (5/7)n

The extension in a string obeying Hooke's law, is x. The speed of sound in the stretched string is v. If the extension in the string is increased to 1.5x, the speed of sound will be-

1.  1.22 v

2.  0.61 v

3.  1.50 v

4.  0.75 v

The equation of plane progressive wave motion is y=a sin 2$\mathrm{\pi }/\mathrm{\lambda }$(vt-x). Velocity of particle is

(1) $y\frac{dv}{dx}$

(2) $v\frac{dy}{dx}$

(3) $-y\frac{dv}{dx}$

(4) $-v\frac{dy}{dx}$

A tuning fork and sonometer give 5 beats per second when the length of the wire is 1 m and 1.05 m respectively. The frequency of fork is -

1. 210 Hz

2. 205 Hz

3. 410 Hz

4. 420 Hz 

A person speaking normally produces a sound of intensity 40 dB at a distance of 1 m. If threshold intensity fo r reasonable audibility is 20 dB, the maximum distance at which he can be heared clearly is:

(1) 4 m

(2) 5 m

(3) 10 m

(4) 20 m