Waves

For a travelling harmonic wave y(x, t) = 2.0 2 (10t - 0.0080x + 0.35), where x and y are in cm and t in s. The phase difference between oscillatory motion of two points separated by a distance of 0.5 m is:

1. 0.08 π rad
2. 0.008 π rad
3. 0.8 π rad
4. 8 π rad

For sound waves, if the number of nodes for the 5th harmonic of an open-ended pipe is n and that for the 9th harmonic of the same pipe with one of its ends closed is m, the ratio nm is

1. 35
2. 59
3. 95
4. 1

A pipe open at both ends has a fundamental frequency f in air. The pipe is now dipped vertically in a water drum to half of its length. The fundamental frequency of the air column is now equal to:

1. 3f2
2. 2f
3. f2
4. f

The displacement of a travelling wave y = C 2 (at - x) where t is time, x is distance and is the wavelength, all in S.I. units. Then the frequency of the wave is

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

The ratio of frequencies of fundamental harmonic produced by an open pipe to that of closed pipe having the same length is

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

If the initial tension on a stretched string is doubled, then the ratio of the initial and final speeds of a transverse wave along the string is

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

An organ pipe filled with a gas at 27 resonates at 400 Hz in its fundamental mode. If it is filled with the same gas at 90 , the resonance frequency at the same mode will be

1. 512 Hz
2. 420 Hz
3. 440 Hz
4. 484 Hz

In a guitar, two strings A and B made of same material are slightly out of tune and produce beats of frequency 6 Hz. When tension in B is slightly decreased, the beat frequency increases. If the frequency of A is 530 Hz, the original frequency of B will be :

1. 524 Hz
2. 536 Hz
3. 537 Hz
4. 523 Hz

A tuning fork is used to produce resonance in a glass tube. The length of the air column in this tube can be adjusted by a variable piston. At room temperature of 27°C two successive resonances are produced at 20 cm and 73 cm of column length. If the frequency of the tuning fork is 320 Hz, the velocity of sound in air at 27°C is

1. 330 m s-1
2. 339 m s-1
3. 350 m s-1
4. 300 m s-1

The fundamental frequency in an open organ pipe is equal to the third harmonic of a closed organ pipe. If the length of the closed organ pipe is 20 cm, the length of the open organ pipe is

1. 13.2 cm
2. 8 cm
3. 12.5 cm
4. 16 cm

The two nearest harmonics of a tube closed at one end and open at other end are 220 Hz and 260 Hz. What is the fundamental frequency of the system ?

1. 20 Hz
2. 30 Hz
3. 40 Hz
4. 10 Hz

Two cars moving in opposite directions approach each other with speed of 22 m s-1 and 16.5 m s-1 respectively. The driver of the first car blows a horn having a frequency 400 Hz. The frequency heard by the driver of the second car is (velocity of sound is 340 m s-1)

1. 361 Hz
2. 411 Hz
3. 448 Hz
4. 350 Hz

An air column, closed at one end open at the other, resonates with a tuning fork when the smallest length of the column is 50 cm. The next larger length of the column resonating with the same tuning fork is

1. 150 cm
2. 200 cm
3. 66.7 cm
4. 100 cm

A uniform rope of length L and mass m1 hangs vertically from a rigid support. A block of mass m2 is attached to the free end of the rope. A transverse pulse of wavelength 1 is produced at the lower end of the rope. The wavelength of the pulse when it reaches the top of the rope is 2. The ratio 2/ 1 is

1. m2m1
2. m1 + m2m1
3. m1m2
4. m1 + m2m2

A siren emitting a sound of frequency 800 Hz moves away from an observer towards a cliff at a speed of 15 m s-1. Then, the frequency of sound that the observer hears in the echo reflected from the cliff is (Take velocity of sound in air = 330 m s-1)

1. 838 Hz
2. 885 Hz
3. 765 Hz
4. 800 Hz

The second overtone of an open organ pipe has the same frequency as the first overtone of a closed pipe L metre long. The length of the open pipe will be

1. L
2. 2L
3. L2
4. 4L

Three sound waves of equal amplitudes have frequencies (n - 1), n, (n + 1). They superimpose to give beats. The number of beats produced per second will be

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

A string is stretched between fixed points separated by 75.0 cm. It is observed to have resonant frequencies of 420 Hz and 315 Hz. There are no other resonant frequencies between these two. The lowest resonant frequency for this string is

1. 10.5 Hz
2. 105 Hz
3. 155 Hz
4. 205 Hz

The fundamental frequency of a closed organ pipe of length 20 cm is equal to the second overtone of an organ pipe open at both the ends. The length of organ pipe open at both the ends is

1. 120 cm
2. 140 cm
3. 80 cm
4. 100 cm

A source of sound S emitting waves of frequency 100 Hz and an observer O are located at some distance from each other. The source is moving with a speed of 19.4 m s-1 at an angle of 60 with the source observer line as shown in the figure. The observer is at rest. The apparent frequency observed by the observer (velocity of sound in air 330 m s-1), is [figure]

1. 106 Hz
2. 97 Hz
3. 100 Hz
4. 103 Hz

If n1, n2 and n3 are the fundamental frequencies of three segments into which a string is divided, then the original fundamental frequency n of the string is given by

1. 1n = 1n1 + 1n2 + 1n3
2. 1 n = 1 n1 + 1 n2 + 1 n3
3. n = n1 + n2 + n3
4. n = n1 + n2 + n3

The number of possible natural oscillations of air column in a pipe closed at one end of length 85 cm whose frequencies lie below 1250 Hz are (Velocity of sound = 340 m s-1)

1. 4
2. 5
3. 7
4. 6

A speeding motorcyclist sees traffic jam ahead of him. He slows down to 36 km hour-1. He finds that traffic has eased and a car moving ahead of him at 18 km hour-1 is honking at a frequency of 1392 Hz. If the speed of sound is 343 m s-1, the frequency of the honk as heard by him will be

1. 1332 Hz
2. 1372 Hz
3. 1412 Hz
4. 1454 Hz

If we study the vibration of a pipe open at both ends, then the following statement is not true.

1. All harmonics of the fundamental frequency will be generated.
2. Pressure change will be maximum at both ends.
3. Open end will be antinode.
4. Odd harmonics of the fundamental frequency will be generated.

A wave travelling in the +ve x-direction having displacement along y-direction as 1 m, wavelength 2 m and frequency of 1 Hz is represented by

1. y = sin(10 x - 20 t)
2. y = sin(2 x + 2 t)
3. y = sin(x - 2t)
4. y = sin(2 x - 2 t)

A source of unknown frequency gives 4 beats/s when sounded with a source of known frequency 250 Hz. The second harmonic of the source of unknown frequency gives five beats per second, when sounded with a source of frequency 513 Hz. The unknown frequency is

1. 240 Hz
2. 260 Hz
3. 254 Hz
4. 246 Hz

The length of the wire between two ends of a sonometer is 100 cm. What should be the positions of two bridges below the wire so that the three segments of the wire have their fundamental frequencies in the ratio 1 : 3 : 5.

1. 150023 cm, 50023 cm
2. 150023 cm, 30023 cm
3. 30023 cm, 150023 cm
4. 150023 cm, 200023 cm

Two sources P and Q produce notes of frequency 660 Hz each. A listener moves from P to Q with a speed of 1 m s-1. If the speed of sound is 330 m/s, then the number of beats heard by the listener per second will be

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

The equation of a simple harmonic wave is given by y = 3 2(50t - x), where x and y are in metres and t is in seconds. The ratio of maximum particle velocity to the wave velocity is

1. 2
2. 32
3. 3
4. 23

A train moving at a speed of 220 m s-1 towards a stationary object, emits a sound of frequency 1000 Hz. Some of the sound reaching the object gets reflected back to the train as echo. The frequency of the echo as detected by the driver of the train is (Speed of sound in air is 330 m s-1)

1. 3500 Hz
2. 4000 Hz
3. 5000 Hz
4. 3000 Hz