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 equation of a wave pulse travelling along x-axis is given by $y=\frac{30}{2+{\left(x-20t\right)}^2}$, x and y are in meters and t is in seconds. The amplitude of the wave pulse is 

1.  5 m

2.  20 m

3.  15 m

4.  30 m

In a stationary wave along a string, the strain is:
1. zero at the antinodes
2. maximum at the antinodes
3. zero at the nodes
4. maximum at the nodes

Equation of the wave is given by y = 0.4 sin(314t - 3.14x), where x and y are in meter and t is in second. The speed of the wave is :

1.  50 m/s

2.  100 m/s

3.  314 m/s

4.  3.14 m/s

How many degrees of freedom the gas molecules have if, under \(\text{STP}\), the gas density \(\rho = 1.3~\text{kg/m}^3\) and the velocity of sound propagation in it is \(330~\text{ms}^{-1}\)${\mathrm{}}^{}$?
1. \(3\)       
2. \(5\)         
3. \(7\)             
4. \(8\)

A wave travelling in the positive \(x\)-direction having maximum displacement along \(y\)-direction as \(1~\text{m},\) wavelength \(2\pi~\text{m}\) and frequency of \(1/ \pi\) Hz is represented by:
1. \(y=\text{sin}(x-2t)\)
2. \(y=\text{sin}(2\pi x-2\pi t)\)
3. \(y=\text{sin}(10\pi x-20\pi t)\)
4. \(y=\text{sin}(2\pi x+2\pi t)\)

When a string is divided into three segments of lengths \(l_1,~l_2\text{ and }l_3,\) the fundamental frequencies of these three segments are \(\nu_1,~\nu_2\text{ and }\nu_3\) respectively. The original fundamental frequency \((\nu)\) of the string is:
1. \(\sqrt{\nu}=\sqrt{\nu_1}+\sqrt{\nu_2}+\sqrt{\nu_3}\)
2. \(\nu=\nu_1+\nu_2+\nu_3\)
3. \(\dfrac{1}{\nu}=\dfrac{1}{\nu_1}+\dfrac{1}{\nu_2}+\dfrac{1}{\nu_3}\)
4. \(\dfrac{1}{\sqrt{\nu}}=\dfrac{1}{\sqrt{\nu_1}}+\dfrac{1}{\sqrt{\nu_2}}+\dfrac{1}{\sqrt{\nu_3}}\)