Waves

A transverse wave on a string is described by y=3 (36t+0.018x+ /4 ), where x, y are in cm and t in seconds. The least distance between the two successive crests in the wave is cm. (Nearest integer) ( =3.14)

The equation of a plane progressive wave is given by y=5 (200t- x150 ) where x and y are in cm and t is in second. The velocity of the wave is m/s.

1. 120
2. 150
3. 200
4. 300

The speed of a longitudinal wave in a metallic bar is 400 m/s. If the density and Young's modulus of the bar material are increased by 0.5% and 1%, respectively then the speed of the wave is changed approximately to m/s.

1. 398
2. 402
3. 401
4. 399

Two tuning forks A and B are sounded together giving rise to 8 beats in 2 s. When fork A is loaded with wax, the beat frequency is reduced to 4 beats in 2 s. If the original frequency of tuning fork B is 380 Hz then original frequency of tuning fork A is Hz.

The fifth harmonic of a closed organ pipe is found to be in unison with the first harmonic of an open pipe. The ratio of lengths of closed pipe to that of the open pipe is 5/x. The value of x is

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

The velocity of sound in air is doubled when the temperature is raised from 0 to . The value of is .

Two loudspeakers (L1 and L2) are placed with a separation of 10 m, as shown in figure. Both speakers are fed with an audio input signal of same frequency with constant volume. A voice recorder, initially at point A, equidistant from both loudspeakers, is moved by 25 m along the line AB while monitoring the audio signal. The measured signal was found to undergo 10 cycles of minima and maxima during the movement. The frequency of the input signal is Hz (Speed of sound in air is 324 m/s and 5 = 2.23) [figure]

In an open organ pipe 3 and 6 are 3rd and 6th harmonic frequencies, respectively. If 6 - 3 = 2200 Hz then length of the pipe is mm. (Take velocity of sound in air is 330 m/s.)

1. 200
2. 225
3. 275
4. 250

Two strings (A, B) having linear densities A = 2 10-4 kg/m and B = 4 10-4 kg/m and lengths LA = 2.5 m and LB = 1.5 m respectively are joined. Free ends of A and B are tied to two rigid supports C and D, respectively creating a tension of 500 N in the wire. Two identical pulses, sent from C and D ends, take time t1 and t2, respectively, to reach the joint. The ratio t1/t2 is:

1. 1.90
2. 1.18
3. 1.08
4. 1.67

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

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