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 $\frac{\pi }{2}$

A tuning fork makes 256 vibrations per second in air. When the velocity of sound is 330 m/s, then the wavelength of the tone emitted is :

1. 0.56 m

2. 0.89 m

3. 1.11 m

4. 1.29 m

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 frequency of a sound wave is n and its velocity is v. If the frequency is increased to 4n, the velocity of the wave will be 

(1) v

(2) 2v

(3) 4v

(4) v/4

The type of waves that can be propagated through solid is :

(1) Transverse

(2) Longitudinal

(3) Both (1) and (2)

(4) None of these

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

A wavelength 0.60 cm is produced in air and it travels at a speed of 300 ms^–1. It will be an 

(1) Audible wave

(2) Infrasonic wave

(3) Ultrasonic wave

(4) None of the above

An observer standing near the seashore observes 54 waves per minute. If the wavelength of the water wave is 10m then the velocity of a water wave is :

(1) 540 ms^-1

(2) 5.4 ms^-1

(3) 0.184 ms^-1

(4) 9 ms^-1