Waves

The amplitude and phase of a wave that is formed by the superposition of two harmonic travelling waves, y1(x, t) = 4 (kx - t) and y2(x, t) = 2 (kx - t + 2 3 ), are: (Take the angular frequency of initial waves same as )

1. [ 3, 6 ]
2. [2 3, 6 ]
3. [6, 2 3 ]
4. [6, 3 ]

Two strings with circular cross section and made of same material, are stretched to have same amount of tension. A transverse wave is then made to pass through both the strings. The velocity of the wave in the first string having the radius of cross section R is v1, and that in the other string having radius of cross section R/2 is v2. Then v2v1 =

1. 8
2. 4
3. 2
4. 2

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