1. The displacement of a travelling wave \( y = C\, sin \left(\frac{2π}{ λ}\right)\) (at \(− x\)) where \(t\) is time, \(x\) is distance and \(λ\) is the wavelength, all in S.I. units. Then the frequency of the wave is

(1).\(2πλ/a\)

(2). \(2πa/λ\)

(3). \(λ/a\)

(4). \(a/λ\)

2. Two slits in Young's double slit experiment are 1.5 mm apart and the screen is placed at a distance of 1m from the slits. If the wavelength of light used is \(600 × 10^{−9}\,m\) then the fringe separation is

(1).\(4 × 10^{−5} m\)

(2). \(9 × 10^{−8} m\)

(3). \(4 × 10^{−7} m\)

(4). \(4 × 10^{−4} m\)

3. Interference pattern can be observed due to superposition of the following waves:
A. \(y = a sinωt\)
B. \(y = a sin2ωt\)
C. \(y = a sin\left(ωt − ϕ\right)\)
D. \(y = a sin 3ωt\).
Choose the correct answer from the options given below.

(1).B and C

(2). B and D

(3). A and C

(4). A and B

4. 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). \(1 : 2\)

5. The 4th overtone of a closed organ pipe is same as that of 3rd overtone of an open pipe. The ratio of the length of the closed pipe to the length of the open pipe is:

(1).\(8 : 9\)

(2). \(9 : 7\)

(3). \(9 : 8\)

(4). \(7 : 9\)

6. 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). \(\sqrt{2} : 1\)

(3). \(1 : \sqrt{2}\)

(4). \(1 : 2\)

7. An organ pipe filled with a gas at \(27^\circ C\) resonates at \(400\, Hz\) in its fundamental mode. If it is filled with the same gas at \(90^\circ C\), the resonance frequency at the same mode will be:

(1).\(512\, Hz\)

(2). \(420\, Hz\)

(3). \(440\, Hz\)

(4). \(484\, Hz\)

8. 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 to \(7\,Hz\). 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). \(523\,Hz\)

9. A tuning fork with frequency \(800\,Hz\) produces resonance in a resonance column tube with upper end open and lower end closed by water surface. Successive resonance are observed at length \(9.75\,cm\), \(31.25\,cm\) and \(52.75\,cm\). The speed of sound in air is

(1).\(500\,m∕s\)

(2). \(156\,m∕s\)

(3). \(344\,m∕s\)

(4). \(172\,m∕s\)

10. 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 \(27^\circ C\) 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 \(27^\circ C\) is

(1).\(330\,ms^{−1}\)

(2). \(339\,ms^{−1}\)

(3). \(350\,ms^{−1}\)

(4). \(300\,ms^{−1}\)

11. 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). \(16\,cm\)

12. 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). \(10\,Hz\)

13. Two cars moving in opposite directions approach each other with speed of \(22\,ms^{−1}\) and \(16.5\,ms^{−1}\) 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 \(340\,ms^{−1}\)]

(1).\(361\, Hz\)

(2). \(411\, Hz\)

(3). \(448\, Hz\)

(4). \(350\, Hz\)

14. A siren emitting a sound of frequency \(800\, Hz\) moves away from an observer towards a cliff at a speed of 15\,ms^{−1}\). Then, the frequency of sound that the observer hears in the echo reflected from the cliff is (Take velocity of sound in air = \(330ms^{−1}\))

(1).\(838\, Hz\)

(2). \(885\, Hz\)

(3). \(765\, Hz\)

(4). \(800\, Hz\)

15. An air column, closed at one end and 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). \(100\, cm\)

16. A uniform rope of length \(L\) and mass \(m_1\) hangs vertically from a rigid support. A block of mass \(m_2\) is attached to the free end of the rope. A transverse pulse of wavelength \(λ_1\) is produced at the lower end of the rope. The wavelength of the pulse when it reaches the top of the rope is \(λ_2\).The ratio \(\frac{λ1}{λ2}\) is

(1).\(\sqrt{\frac{m2}{m1}}\)

(2). \(\sqrt{\frac{m1 + m2}{m1}}\)

(3). \(\sqrt{\frac{m1}{m2}}\)

(4). \(\sqrt{\frac{m1 + m2}{m2}}\)

17. 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). \(\frac{L}{2}\)

(4). \(4L\)

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

(1).\(1\)

(2). \(4\)

(3). \(3\)

(4). \(2\)

19. 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). \(205\, Hz\)

20. \(4.0\, g\) of a gas occupies \(22.4\, litres\) at NTP. The specific heat capacity of the gas at constant volume is \(5.0\,J K^{−1}mol^{ −1}\). If the speed of sound in this gas at NTP is \(952\,ms^{−1}\), then the heat capacity at constant pressureis (Take gas constant \(R = 8.3\,J K^{−1}mol^{ −1}\))

(1).\(7.0\,J K^{ −1}mol^{ −1}\)

(2). \(8.5\,J K^{ −1}mol^{ −1}\)

(3). \(8.0\,J K^{ −1}mol^{ −1}\)

(4). \(7.5\,J K^{ −1}mol^{ −1}\)

21. 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 \(19.4\,ms^1\) at an angle of \(60^\circ\) 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 \(330\,ms^{−1}\)), is

(1).\(106\, Hz\)

(2). \(97\, Hz\)

(3). \(100\, Hz\)

(4). \(103\, Hz\)

22. 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). \(100\, cm\)

23. 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 = \(340\,ms^{−1}\))

(1).\(4\)

(2). \(5\)

(3). \(7\)

(4). \(6\)

24. A speeding motorcyclist sees traffic jam ahead of him. He slows down to \(36\, kmhour^{−1}\). He finds that traffic has eased and a car moving ahead of him at \(18\, kmhour^{−1}\) is honking at a frequency of \(1392\, Hz\). If the speed of sound is \(343\, ms^{−1}\), the frequency of the honk as heard by him will be

(1).\(1332\, Hz\)

(2). \(1372\, Hz\)

(3). \(1412\, Hz\)

(4). \(1454\, Hz\)

25. 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).\(\frac{1}{n} = \frac{1}{n_1} + \frac{1}{n_2} + \frac{1}{n_3}\)

(2). \(\frac{1}{\sqrt{n}} = \frac{1}{\sqrt{n_1}} + \frac{1}{\sqrt{n_2}} + \frac{1}{\sqrt{n_3}}

(3). \(\sqrt{n} = \sqrt{n_1} + \sqrt{n_2} + \sqrt{n_3}

(4). \(n = n_1 + n_2 + n_3

26. When two displacements represented by \(y_1\,=\, a\, sin\, \left(\omega\,t\right)\) and \(y_2\,=\, b\, cos\, \left(\omega\,t\right)\)are superimposed the motion is:

(1).not a simple harmonic

(2). simple harmonic with amplitude \(\displaystyle \frac{a}{b}\)

(3). simple harmonic with amplitude \(\displaystyle \sqrt{a^2\,+\,b^2}\)

(4). simple harmonic with amplitude \(\displaystyle \frac{\left(a\,+\,b\right)}{2}\)

27. 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).\(2f\)

(2). \(\displaystyle \frac{f}{2}\)

(3). \(f\)

(4). \(\displaystyle \frac{3f}{2}\)