Waves

Two harmonic waves moving in the same direction superimpose to form a wave x = a (1.5t) (50.5t) where t is in seconds. Find the period with which they beat. (close to nearest integer)

1. 1 s
2. 4 s
3. 2 s
4. 6 s

The equation of a wave travelling on a string is y = [20 x + 10 t], where x and t are distance and time in SI units. The minimum distance between two points having the same oscillating speed is :

1. 10 cm
2. 2.5 cm
3. 20 cm
4. 5.0 cm

Consider the sound wave travelling in ideal gases of He, CH4, and CO2. All the gases have the same ratio P , where P is the pressure and is the density. The ratio of the speed of sound through the gases VHe : VCH4 : VCO2 is given by

1. 75 : 53 : 43
2. 53 : 43 : 43
3. 53 : 43 : 75
4. 43 : 53 : 75

In an experiment with a closed organ pipe, it is filled with water by ( 15 )th of its volume. The frequency of the fundamental note will change by

1. 20\%
2. 25\%
3. -20\%
4. -25\%

Displacement of a wave is expressed as x(t)=5 (628t+ 2 )m. The wavelength of the wave when its velocity is 300 m/s is : ( =3.14)

1. 0.33 m
2. 0.5 m
3. 3 m
4. 5 m

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