Wave Motion questions with solutions

Showing 1–10 of 481 questions

• MCQeasyWave Motion

  Two coherent sources of sound, S₁ and S₂, produce sound waves of the same wavelength, λ = 1 m, in phase. S₁ and S₂ are placed 1.5 m apart (see fig.) A listener, located at L, directly in front of S₂ finds that the intensity is at a minimum when he is 2m away from S₂. The listener moves away from S₁, keeping his distance from S₂ fixed. The adjacent maximum of intensity is observed when the listener is at a distance d from S₁. Then, d is:

  

  Options

  • Option A

    12m

  • Option B

    3m

  • Option C

    5m

  • Option D

    2m

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• NumericeasyWave MotionTransverse Waves on a Stretched String and Wave Speed

  A transverse wave travels along a string with speed 40 m/s. The string has linear mass density 0.025 kg/m. If the tension in the string is N newtons, find N.

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• NumericmediumWave Motion

  A string, fixed at both ends, vibrates in a resonant mode with a separation of 2.0 cm between the consecutive nodes. For the next higher resonant frequency, this separation is reduced to 1.6 cm. Find the length of the string.

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• MCQmediumWave MotionWave Motion and General Equation of Travelling Waves

  Which of the following displacement expressions can represent an undistorted travelling wave moving with a single constant speed?

  Options

  • Option A

    y = A sin(kx-ωt)

  • Option B

    y = A exp[-(x-vt)²/a²]

  • Option C

    y = A cos[k(x+vt)]

  • Option D

    All of the above

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• Multi-correcteasyWave Motion

  Two loudspeakers M and N are 20 m apart and emit 118 Hz and 121 Hz. A car moves along the perpendicular bisector from P through midpoint Q to R at 60 km h⁻¹; P and R are each 1800 m from Q. Let ν(t) be the beat frequency in the car. Compare the beat frequencies at P, Q and R as indicated in the options. Take sound speed = 330 m s⁻¹.

  Select all that apply

  • Option A

    
  • Option B

    
  • Option C

    The rate of change in beat frequency is maximum when the car passes through Q

  • Option D

    vP + vR = 2vQ

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• MCQmediumWave MotionWave Motion and General Equation of Travelling Waves

  At t = 0, a localized pulse on a string has the shape y(x,0) = A/[1+(x/a)²]. It propagates towards the negative x-direction with speed v without changing shape. Which expression correctly represents the pulse at time t?

  Options

  • Option A

    y = A/{1+[(x-vt)/a]²}

  • Option B

    y = A/{1+[(x+vt)/a]²}

  • Option C

    y = A/{1+(x/a)²+vt}

  • Option D

    y = A/{1+[(vt-x)/a]}

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• MCQmediumWave Motion

  A travelling pulse is f(x, t) = A exp{[2abxt - a²x² - b²t²]/c²}, where A, a, b and c are positive constants. Find the pulse speed.

  Options

  • Option A

    b/a

  • Option B

    2b/a

  • Option C

    bc/a

  • Option D

    b/(2a)

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• MCQmediumWave Motion

  A mass of 20 kg is hanging with support of two strings of same linear mass density. Now pulses are generated in both strings at same time near the joint at mass. Ratio of time, taken by a pulse travel through string 1 to that taken by pulse on string 2 is

  

  Options

  • Option A

    4/3

  • Option B

    2/√3

  • Option C

    8/(3√3)

  • Option D

    3/(2√3)

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• Multi-correctmediumWave MotionSound Waves: Wave Equation, Propagation and Speed of Sound

  Which expressions are correct in the standard ideal approximations for the speed of sound?

  Select all that apply

  • Option A

    In a fluid, v = √(B/ρ).

  • Option B

    In a thin solid rod, v = √(Y/ρ).

  • Option C

    In an ideal gas, v = √(γP/ρ).

  • Option D

    In an ideal gas, v = √(γRT/M).

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• NumericmediumWave MotionBeats, Loudness, Pitch and Characteristics of Sound

  Two tuning forks A and B produce 10 beats per second. Fork A is known to have frequency 450 Hz. Wax is added only to fork A, lowering its frequency by 6 Hz, and the beat frequency becomes 16 beats per second. If the frequency of fork B is N Hz, find N.

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