Waves

In the resonance experiment, two air columns (closed at one end) of 100 cm and 120 cm long, give 15 beats per second when each one is sounding in the respective fundamental modes. The velocity of sound in the air column is:

1. 370 m/s
2. 340 m/s
3. 335 m/s
4. 360 m/s

A sinusoidal wave of wavelength 7.5 cm travels a distance of 1.2 cm along the x-direction in 0.3 sec. The crest P is at x = 0 at t = 0 sec and maximum displacement of the wave is 2 cm. Which equation correctly represents this wave?

1. y = 2 (0.83x - 3.35t) cm
2. y = 2 (0.83x - 3.5t) cm
3. y = 2 (0.13x - 0.5t) cm
4. y = 2 (3.35x - 0.83t) cm

Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R In the light of the above statements, choose the correct answer from the options given below

1. Both A and R are true and R is the correct explanation of A
2. A is false but R is true
3. A is true but R is false
4. Both A and R are true but R is NOT the correct explanation of A

The equation of a transverse wave travelling along a string is y(x,t)=4.0 [20 10-3x+600t ]mm, where x is in mm and t is in second. The velocity of the wave is :

1. -60 m/s
2. +60 m/s
3. +30 m/s
4. -30 m/s

A closed organ and an open organ tube are filled by two different gases having same bulk modulus but different densities 1 and 2, respectively. The frequency of 9th harmonic of closed tube is identical with 4th harmonic of open tube. If the length of the closed tube is 10 cm and the density ratio of the gases is 1: 2=1:16, then the length of the open tube is :

1. 157 cm
2. 209 cm
3. 207 cm
4. 159 cm