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A Sine Wave is Travelling in a Medium. the Minimum Distance Between the Two Particles, Always Having Same Speed, is - Physics

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प्रश्न

A sine wave is travelling in a medium. The minimum distance between the two particles, always having same speed, is

पर्याय

  • \[\lambda/4\]

  • \[\lambda/3\]

  • \[\lambda/2\]

  • \[\lambda\]

MCQ
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उत्तर

\[\lambda/2\]

A sine wave has a maxima and a minima and the particle displacement has phase difference of π radians. The speeds at the maximum point and at the minimum point are same although the direction of motion are different. The difference between the positions of maxima and minima is equal to 
\[\lambda/2\]

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The Speed of a Travelling Wave
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 15: Wave Motion and Waves on a String - MCQ [पृष्ठ ३२२]

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एचसी वर्मा Concepts of Physics Vol. 1 [English] Class 11 and 12
पाठ 15 Wave Motion and Waves on a String
MCQ | Q 1 | पृष्ठ ३२२

संबंधित प्रश्‍न

(i) For the wave on a string described in Exercise 15.11, do all the points on the string oscillate with the same (a) frequency, (b) phase, (c) amplitude? Explain your answers. (ii) What is the amplitude of a point 0.375 m away from one end?


A steel rod 100 cm long is clamped at its middle. The fundamental frequency of longitudinal vibrations of the rod is given to be 2.53 kHz. What is the speed of sound in steel?


A SONAR system fixed in a submarine operates at a frequency 40.0 kHz. An enemy submarine moves towards the SONAR with a speed of 360 km h–1. What is the frequency of sound reflected by the submarine? Take the speed of sound in water to be 1450 m s–1.


A sine wave is travelling in a medium. A particular particle has zero displacement at a certain instant. The particle closest to it having zero displacement is at a distance


A wave pulse, travelling on a two-piece string, gets partially reflected and partially transmitted at the junction. The reflected wave is inverted in shape as compared to the incident one. If the incident wave has wavelength λ and the transmitted wave λ'


Two wires A and B, having identical geometrical construction, are stretched from their natural length by small but equal amount. The Young modules of the wires are YA and YB whereas the densities are \[\rho_A \text{ and }   \rho_B\]. It is given that YA > YB and \[\rho_A  >  \rho_B\]. A transverse signal started at one end takes a time t1 to reach the other end for A and t2 for B.


Two sine waves travel in the same direction in a medium. The amplitude of each wave is A and the phase difference between the two waves is 120°. The resultant amplitude will be


The equation of a wave travelling on a string is:

\[y = \left( 0 \cdot 10  \text{ mm } \right)  \sin\left[ \left( 31 \cdot 4  m^{- 1} \right)x + \left( 314  s^{- 1} \right)t \right]\]

  1. In which direction does the wave travel?
  2. Find the wave speed, the wavelength and the frequency of the wave.
  3. What is the maximum displacement and the maximum speed of a portion of the string?

Two long strings A and B, each having linear mass density
\[1 \cdot 2 \times  {10}^{- 2}   kg   m^{- 1}\] , are stretched by different tensions 4⋅8 N and 7⋅5 N respectively and are kept parallel to each other with their left ends at x = 0. Wave pulses are produced on the strings at the left ends at t = 0 on string A and at t = 20 ms on string B. When and where will the pulse on B overtake that on A?


A 200 Hz wave with amplitude 1 mm travels on a long string of linear mass density 6 g m−1 kept under a tension of 60 N. (a) Find the average power transmitted across a given point on the string. (b) Find the total energy associated with the wave in a 2⋅0 m long portion of the string.


A steel wire fixed at both ends has a fundamental frequency of 200 Hz. A person can hear sound of maximum frequency 14 kHz. What is the highest harmonic that can be played on this string which is audible to the person?


Figure shows an aluminium wire of length 60 cm joined to a steel wire of length 80 cm and stretched between two fixed supports. The tension produced is 40 N. The cross-sectional area of the steel wire is 1⋅0 mm2 and that of the aluminium wire is 3⋅0 mm2. What could be the minimum frequency of a tuning fork which can produce standing waves in the system with the joint as a node? The density of aluminium is 2⋅6 g cm−3 and that of steel is 7⋅8 g cm−3.


The equation for the vibration of a string, fixed at both ends vibrating in its third harmonic, is given by
\[y = \left( 0 \cdot 4  cm \right)  \sin\left[ \left( 0 \cdot 314  {cm}^{- 1} \right)  x \right]  \cos  \left[ \left( 600\pi  s^{- 1} \right)  t \right]\]
(a) What is the frequency of vibration? (b) What are the positions of the nodes? (c) What is the length of the string? (d) What is the wavelength and the speed of two travelling waves that can interfere to give this vibration?


A 2⋅00 m-long rope, having a mass of 80 g, is fixed at one end and is tied to a light string at the other end. The tension in the string is 256 N. (a) Find the frequencies of the fundamental and the first two overtones. (b) Find the wavelength in the fundamental and the first two overtones.


A man standing unsymmetrical position between two mountains and fires a gun. He hears the first echo after 1.5 s and the second echo after 2.5 s. If the speed of sound in air is 340 m/s, then the distance between the mountains will be ______ 


What is the interference of sound waves? 


A bat emits an ultrasonic sound of frequency 1000 kHz in the air. If the sound meets a water surface, what is the wavelength of the the reflected sound? The speed of sound in air is 340 m s–1 and in water 1486 m s–1.


For the travelling harmonic wave

y (x, t) = 2.0 cos 2π (10t – 0.0080x + 0.35)

Where x and y are in cm and t in s. Calculate the phase difference between oscillatory motion of two points separated by a distance of 4 m.


A steel wire has a length of 12 m and a mass of 2.10 kg. What will be the speed of a transverse wave on this wire when a tension of 2.06 × 104N is applied?


Given below are some functions of x and t to represent the displacement of an elastic wave.

  1. y = 5 cos (4x) sin (20t)
  2. y = 4 sin (5x – t/2) + 3 cos (5x – t/2)
  3. y = 10 cos [(252 – 250) πt] cos [(252 + 250)πt]
  4. y = 100 cos (100πt + 0.5x)

State which of these represent

  1. a travelling wave along –x direction
  2. a stationary wave
  3. beats
  4. a travelling wave along +x direction.

Given reasons for your answers.


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