Wave Motion & Waves on String PYQs Set 1 (PDF)

Set 1 of 5 · Questions 1-30 of 122

In the print window choose “Save as PDF”. The file prints without a web address or date line.

Mere Teacher · Previous Year Questions NEET Physics · Wave Motion & Waves on String · Set 1 (Q1-30)
Scan or visit mereteacher.com for free PYQ practice, timed CBT tests, step-by-step solutions and BroBot AI. Answers and solutions are free with a sign-up.
1. $The equation of the progressive wave is Y = 3 sin (π (\frac{t}{3} - \frac{x}{5}) + \frac{π}{4}) where x and Y are in metre and time in second. Which of the following is correct?$ (1) $velocity V = 1.5 m / s$ (2) $amplitude A = 3 cm$ (3) $frequency F = 0.2 Hz$ (4) $wavelength λ = 10 m$ 2. $A heavy ball of mass M is suspended from the ceiling of a car by a light string of mass m (m ≪ M). When the car is at rest, the speed of transverse waves in the string is 60 ms^{- 1} . When the car has acceleration a, the wave-speed increases to 60.5 ms^{- 1} . The value of a, in terms of gravitational acceleration g, is closest to:$ (1) $\frac{g}{30}$ (2) $\frac{g}{20}$ (3) $\frac{g}{5}$ (4) $\frac{g}{10}$ 3. $A transverse wave is represented by y=2sin (ωt - kx) cm. The value of wavelength (in cm) for which the wave velocity becomes equal to the maximum particle velocity, will be;$ (1) $4 π$ (2) $2 π$ (3) $π$ (4) $2$ 4. $Two harmonic waves moving in the same direction superimpose to form a wave x = acos (1.5 t) cos (50.5 t) where t is in seconds. Find the period with which they beat. (close to nearest integer)$ (1) $1 s$ (2) $4 s$ (3) $2 s$ (4) $6 s$ 5. $The equation of a stationary wave is y = 2 sin (\frac{πx}{15}) cos (48 πt) . The distance between a node and its next antinode is$ (1) $22.5 units$ (2) $7.5 units$ (3) $30 units$ (4) $1.5 units$ 6. $The maximum particle velocity in a wave motion is half the wave velocity. Then the amplitude of the wave is equal to$ (1) $λ /4 π$ (2) $2 λ / π$ (3) $λ /2 π$ (4) $λ$ 7. $A transverse wave is represented by y = A sin (ωt - kx) . For what value of the wavelength is the wave velocity equal to the maximum particle velocity?$ (1) $πA /2$ (2) $πA$ (3) $2 πA$ (4) $A$ 8. $A point performs simple harmonic oscillation of period and the equation of motion is given by . After the elapse of what fraction of the time period the velocity of the point will be equal to halfofits maximum velocity?$ (1) $T /3$ (2) $T/12$ (3) $T /8$ (4) $T /6$ 9. $In a sinusoidal wave, the time required for a particular point to move from maximum displacement to zero displacement is 0.170 s . The frequency of wave is$ (1) $0.73 Hz$ (2) $0.36 Hz$ (3) $1.47 Hz$ (4) $2.94 Hz$ 10. $The equation of a wave is given by y = 10 sin (\frac{2 π}{45} t + α) . If the displacement is 5 cm at t = 0, then the total phase at t = 7.5 sec is$ (1) $π /3$ (2) $π /2$ (3) $π /6$ (4) $π$ 11. $Two periodic waves of intensities I_{1} and I_{2} pass through a region at the same time in the same direction. The sum of the maximum and minimum intensities is$ (1) $(l_{1} - l_{2})^{2}$ (2) $2 (I_{1} + I_{2})$ (3) $I_{1} + I_{2}$ (4) $(l_{1} + l_{2})^{2}$ 12. $A uniform wire of length L, diameter D and density ρ is stretched under a tension T . The correct relation between its fundamental frequency ' f', the length L and the diameter D is$ (1) $f \propto \frac{1}{LD}$ (2) $f \propto \frac{1}{L D}$ (3) $f \propto \frac{1}{D ^{2}}$ (4) $f \propto \frac{1}{L D ^{2}}$ 13. $Statement - 1: Two longitudinal waves given by equations: y_{1} (x, t) = 2a sin (ꞷt - kx) and y_{2} (x, t) = a sin (2ꞷt - 2kx) will have equal intensity. Statement - 2: Intensity of waves of given frequency in same medium is proportional to square of amplitude only.$ (1) $Statement-1 is true, statement-2 is false.$ (2) $Statement-1 is true, statement-2 is true, statement-2 is the correct explanation of statment-1$ (3) $Statement-1 is true, statement-2 is true, statement-2 is not the correct explanation of statement-1$ (4) $Statement-1 is false, statement-2 is true.$ 14. $Two identical piano wires, kept under the same tension have a fundamental frequency of 600 Hz. The fractional increase in the tension ofone ofthe wires which will lead to occurrence of 6 beats/s when both the wires oscillate together would be$ (1) $0.01$ (2) $0.02$ (3) $0.03$ (4) $0.04$ 15. $A string of length 1 m and mass 5 g is fixed at both ends. The tension in the string is 8.0 N The string is set into vibration using an external vibrator of frequency 100 Hz . The separation between successive nodes on the string is close to:$ (1) $10.0 cm$ (2) $33.3 cm$ (3) $16.6 cm$ (4) $20.0 cm$ 16. $Speed of a transverse wave on a straight wire (mass 6 g, length 60 cm and area of cross-section 1.0 m m^{2}) is 90 m s^{- 1} . If the Youngs modules of wire is 16 \times 10^{11} N m^{- 2}, the extension of wire over its natural length is:$ (1) $0.03 mm$ (2) $0.02 mm$ (3) $0.01 mm$ (4) $0.04 mm$ 17. $A uniform rope of length L and mass m_{1} hangs vertically from a rigid support. A block of mass m_{2} is attached to the free end of the rope. A transverse pulse ofwavelength λ_{1} is produced at the lower end ofthe rope. The wavelength of the pulse when it reaches the top of the rope is λ_{2} . The ratio λ_{2} / λ_{1} is$ (1) $\frac{m _{2}}{m _{1}}$ (2) $\frac{m _{1} + m _{2}}{m _{1}}$ (3) $\frac{m _{1}}{m _{2}}$ (4) $\frac{m _{1} + m _{2}}{m _{2}}$ 18. $y = 3 sin π (\frac{t}{2} - \frac{x}{4}) represents an equation of a progressive wave, where t is in second and x is in metre. The distance travelled by the wave in 5 seconds is$ (1) $8 m$ (2) $10 m$ (3) $5 m$ (4) $32 m .$ 19. $A metallic wire of 1 m length has a mass of 10 \times 10^{- 3} kg . If a tension of 100 N is applied to a wire, what is the speed of transverse wave?$ (1) $200 m s^{- 1}$ (2) $100 m s^{- 1}$ (3) $0.1 m s^{- 1}$ (4) $10 m s^{- 1}$ 20. $Two waves are represented by the equations y_{1} = a sin(ꞷt + kx + 0.57)m and y_{2} = a cos(ꞷt + kx)m, where x is in meter and t in sec. The phase difference between them is:$ (1) $1.0 radian$ (2) $1.25 radian$ (3) $1.57 radian$ (4) $0.57 radian$ 21. $Two strings A and B of same material are stretched by same tension. The radius of the string A is double the radius of string B . Transverse wave travels on string A with speed V_{A} and on string B with speed V_{B} . The ratio \frac{V _{A}}{V _{B}} is$ (1) $\frac{1}{4}$ (2) $\frac{1}{2}$ (3) $2$ (4) $4$ 22. $A travelling wave is described by the equation y(x, t) = [0.05 sin (8x - 4t] m The velocity of the wave is: [all the quantities are in SI unit]$ (1) $4 m s^{- 1}$ (2) $2 m s^{- 1}$ (3) $0.5 m s^{- 1}$ (4) $8 m s^{- 1}$ 23. $Standing waves are produced in 10 m long stretched string. If the string vibrates in 5 segments and wave velocity is 20 m / s, the frequency is$ (1) $5 Hz$ (2) $10 Hz$ (3) $2 Hz$ (4) $4 Hz$ 24. $A string is cut into three parts, having fundamental frequencies n_{1}, n_{2}, n_{3} respectively. Then original fundamental frequency n related by the expression as$ (1) $\frac{1}{n} = \frac{1}{n _{1}} + \frac{1}{n _{2}} + \frac{1}{n _{3}}$ (2) $n = n_{1} \times n_{2} \times n_{3}$ (3) $n = n_{1} + n_{2} + n_{3}$ (4) $n = n_{1} + n_{2} + n_{3} 3.$ 25. $Equation of progressive wave is given by y = 4 sin (π (\frac{t}{5} - \frac{x}{9}) + \frac{π}{6}) wherey, x are in cm and t is in seconds. Then which ofthe following is correct?$ (1) $v = 5 cm$ (2) $λ = 18 cm$ (3) $a = 0.04 cm$ (4) $f = 50 Hz$ 26. $A string is stretched between fixed points separated by 75.0 cm. It is observed to have resonant frequencies of 420 Hz and 315 Hz. There are no other resonant frequencies between these two. The lowest resonant frequency for this string is$ (1) $10.5 Hz$ (2) $105 Hz$ (3) $155 Hz$ (4) $205 Hz$ 27. $The equation of a wave on a string of linear mass density 0.04 kg m^{-1} is given by y = 0.02 (m) sin (2 π (\frac{t}{0.04 ( s )} - \frac{x}{0.50 ( m )})) . The tension in the string is:$ (1) $4.0 N$ (2) $12.5 N$ (3) $0.5 N$ (4) $6.25 N$ 28. $The equation of the progressive wave is y = asin 2 π (nt - \frac{x}{5}) . The ratio of maximum particle velocity to wave velocity is$ (1) $\frac{πa}{5}$ (2) $\frac{2 πa}{5}$ (3) $\frac{3 πa}{5}$ (4) $\frac{4 πa}{5}$ 29. $In the wave equation y = 0.5 sin \frac{2 π}{λ} (400 t - x) m the velocity of the wave will be:$ (1) $200 m/s$ (2) $2002 m / s$ (3) $400 m/s$ (4) $4002 m/s$ 30. $The equation of a wave travelling on a string is y = sin [20 πx + 10 πt], where x and t are distance and time in SI units. The minimum distance between two points having the same oscillating speed is:$ (1) $10 cm$ (2) $2.5 cm$ (3) $20 cm$ (4) $5.0 cm$