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.  $\sqrt{6}/5$

A man drops a stone into a lake from the top of a tower that is \(500~\text{m}\) high. If the speed of sound in air is \(340~\text{m/s},\) approximately how long after releasing the stone will he hear the sound of the splash? \(\left(\text{take }g=10~\text{m/s}^2\right)\)
1. \(11.5~\text{s}\)
2. \(21~\text{s}\)
3. \(10~\text{s}\)
4. \(14~\text{s}\)

At what temperature velocity of sound is double than that of at 0°C 

1. 819 K

2. 819°C

3. 600°C

4. 600 K

If the density of oxygen is 16 times that of hydrogen, what will be the ratio of their corresponding velocities of sound waves :

1. 1 : 4

2. 4 : 1

3. 16 : 1

4. 1 : 16

The phase difference between two points separated by 1m in a wave of frequency 120 Hz is 90°. The wave velocity is :

1. 180 m/s

2. 240 m/s

3. 480 m/s

4. 720 m/s

The echo of a gunshot is heard 8 sec. after the gun is fired. How far from him is the surface that reflects the sound? (velocity of sound in air = 350 m/s) :

1. 1400 m

2. 2800 m

3. 700 m

4. 350 m

The velocity of sound in air is:

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