Two waves are represented by the equations $y_1=a\sin \omega t$ and $y_2=a\cos \omega t.$ The first wave 

(1) Leads the second by $\pi$

(2) Lags the second by $2\pi$

(3) Leads the second by $\frac{\pi }{2}$

(4) Lags the second by $\frac{\pi }{2}$

The distance between two consecutive crests in a wave train produced in a string is 5 cm. If 2 complete waves pass through any point per second, the velocity of the wave is :

1. 10 cm/sec

2. 2.5 cm/sec

3. 5 cm/sec

4. 15 cm/sec

The ratio of the speed of sound in nitrogen gas to that in helium gas, at 300 K is 

1.  $\sqrt{2/7}$

2.  $\sqrt{1/7}$

3.  $\sqrt{3}/5$

4.  $\sqrt{6}/5$

The speed of a wave in a certain medium is 960 m/s. If 3600 waves pass over a certain point of the medium in 1 minute, the wavelength is :

(1) 2 metres

(2) 4 metres

(3) 8 metres

(4) 16 metres

A source of the sound of frequency 600 Hz is placed inside water. The speed of sound in water is 1500 m/s and in the air is 300 m/s. The frequency of sound recorded by an observer who is standing in the air is : 

1. 200 Hz

2. 3000 Hz

3. 120 Hz

4. 600 Hz

A wave of the frequency of 500 Hz has a velocity of 360 m/sec. The distance between two nearest points 60° out of phase is :

(1) 0.6 cm

(2) 12 cm

(3) 60 cm

(4) 120 cm

Equation of a progressive wave is given by

$y=0.2\cos \left(0.04\pi t+0.02\pi x-\frac{{\displaystyle \pi }}{{\displaystyle 6}}\right)$

The distance is expressed in cm and time in second. What will be the minimum distance between two particles having the phase difference of π/2 :

1. 4 cm

2. 8 cm

3. 25 cm

4. 12.5 cm

Which one of the following does not represent a traveling wave :

1. $y=\sin (x-vt)$

2. $y=y_m\sin k(x+vt)$

3. $y=y_m\sin (x-vt)$

4. $y=f(x^2-v{t}^2)$

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