हिंदी

Choose the correct option: Which of the following equations represents a wave travelling along Y-axis?

Advertisements
Advertisements

प्रश्न

Choose the correct option:

Which of the following equations represents a wave travelling along Y-axis? 

विकल्प

  • x = A sin(ky – ωt)

  • y = A sin(kx – ωt)

  • y = A sin(ky) cos(ωt)

  • y = A cos(ky) sin(ωt)

MCQ
Advertisements

उत्तर

x = A sin(ky – ωt)

Explanation:

The direction of the displacement of a wave is perpendicular to the wave's motion direction in transverse waves. When a transverse wave is moving in a y-direction, then the displacement of the wave will be in the x-direction, and if the wave which is travelling along the x-axis, its displacement will be towards the y-axis.

The equation for the wave travelling along the y-axis is x = A sin(ky – ωt)

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 6: Superposition of Waves - Exercises [पृष्ठ १५६]

APPEARS IN

बालभारती Physics [English] Standard 12 Maharashtra State Board
अध्याय 6 Superposition of Waves
Exercises | Q 1.4 | पृष्ठ १५६
एचसी वर्मा Concepts of Physics Volume 1 and 2 [English]
अध्याय 15 Wave Motion and Waves on a String
MCQ | Q 3 | पृष्ठ ३२२

संबंधित प्रश्न

Use the formula `v = sqrt((gamma P)/rho)` to explain why the speed of sound in air increases with humidity.


You have learnt that a travelling wave in one dimension is represented by a function y= f (x, t)where x and t must appear in the combination x – v t or x + v t, i.e. y = f (x ± v t). Is the converse true? Examine if the following functions for y can possibly represent a travelling wave:

(a) `(x – vt )^2`

(b) `log [(x + vt)/x_0]`

(c) `1/(x + vt)`


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 transmitted sound? The speed of sound in air is 340 m s–1 and in water 1486 m s–1.


A hospital uses an ultrasonic scanner to locate tumours in a tissue. What is the wavelength of sound in the tissue in which the speed of sound is 1.7 km s–1? The operating frequency of the scanner is 4.2 MHz.


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 `(3λ)/4`.


A wire stretched between two rigid supports vibrates in its fundamental mode with a frequency of 45 Hz. The mass of the wire is 3.5 × 10–2 kg and its linear mass density is 4.0 × 10–2 kg m–1. What is (a) the speed of a transverse wave on the string, and (b) the tension in the string?


A metre-long tube open at one end, with a movable piston at the other end, shows resonance with a fixed frequency source (a tuning fork of frequency 340 Hz) when the tube length is 25.5 cm or 79.3 cm. Estimate the speed of sound in air at the temperature of the experiment. The edge effects may be neglected.


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 train, standing at the outer signal of a railway station blows a whistle of frequency 400 Hz in still air. (i) What is the frequency of the whistle for a platform observer when the train (a) approaches the platform with a speed of 10 m s–1, (b) recedes from the platform with a speed of 10 m s–1? (ii) What is the speed of sound in each case? The speed of sound in still air can be taken as 340 m s–1.


A train, standing in a station-yard, blows a whistle of frequency 400 Hz in still air. The wind starts blowing in the direction from the yard to the station with at a speed of 10 m s–1. What are the frequency, wavelength, and speed of sound for an observer standing on the station’s platform? Is the situation exactly identical to the case when the air is still and the observer runs towards the yard at a speed of 10 m s–1? The speed of sound in still air can be taken as 340 m s–1.


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.


Earthquakes generate sound waves inside the earth. Unlike a gas, the earth can experience both transverse (S) and longitudinal (P) sound waves. Typically the speed of wave is about 4.0 km s–1, and that of wave is 8.0 km s–1. A seismograph records and waves from an earthquake. The first wave arrives 4 min before the first wave. Assuming the waves travel in straight line, at what distance does the earthquake occur?


Two strings A and B, made of same material, are stretched by same tension. The radius of string A is double of the radius of B. A transverse wave travels on A with speed `v_A` and on B with speed `v_B`. The ratio `v_A/v_B` is ______.


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'


A sonometer wire of length l vibrates in fundamental mode when excited by a tuning fork of frequency 416. Hz. If the length is doubled keeping other things same, the string will ______.


A sonometer wire supports a 4 kg load and vibrates in fundamental mode with a tuning fork of frequency 416. Hz. The length of the wire between the bridges is now doubled. In order to maintain fundamental mode, the load should be changed to


A pulse travelling on a string is represented by the function \[y = \frac{a^2}{\left( x - \nu t \right)^2 + a^2},\] where a = 5 mm and ν = 20 cm-1. Sketch the shape of the string at t = 0, 1 s and 2 s. Take x = 0 in the middle of the string.


The displacement of the particle at x = 0 of a stretched string carrying a wave in the positive x-direction is given f(t) = A sin (t/T). The wave speed is  v. Write the wave equation.


A wave propagates on a string in the positive x-direction at a velocity \[\nu\] \[t =  t_0\] is given by \[g\left( x, t_0 \right) = A  \sin  \left( x/a \right)\]. Write the wave equation for a general time t.


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?

A wave travels along the positive x-direction with a speed of 20 m s−1. The amplitude of the wave is 0⋅20 cm and the wavelength 2⋅0 cm. (a) Write the suitable wave equation which describes this wave. (b) What is the displacement and velocity of the particle at x= 2⋅0 cm at time = 0 according to the wave equation written? Can you get different values of this quantity if the wave equation is written in a different fashion?


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?


Two waves, travelling in the same direction through the same region, have equal frequencies, wavelengths and amplitudes. If the amplitude of each wave is 4 mm and the phase difference between the waves is 90°, what is the resultant amplitude?


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?


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 40 cm wire having a mass of 3⋅2 g is stretched between two fixed supports 40⋅05 cm apart. In its fundamental mode, the wire vibrates at 220 Hz. If the area of cross section of the wire is 1⋅0 mm2, find its Young modulus.


Following figure shows a string stretched by a block going over a pulley. The string vibrates in its tenth harmonic in unison with a particular tuning for. When a beaker containing water is brought under the block so that the block is completely dipped into the beaker, the string vibrates in its eleventh harmonic. Find the density of the material of the block.


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 string 1 m long is fixed at one end. The other end is moved up and down with a frequency of 20 Hz. Due to this, a stationary wave with four complete loops gets produced on the string. Find the speed of the progressive wave which produces the stationary wave. 


Use the formula `v = sqrt((gamma P)/rho)` to explain why the speed of sound in air is independent of pressure.


Use the formula `v = sqrt((gamma P)/rho)` to explain why the speed of sound in air increases with temperature.


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 sound wave is passing through air column in the form of compression and rarefaction. In consecutive compressions and rarefactions ______.


A string of mass 2.5 kg is under a tension of 200 N. The length of the stretched string is 20.0 m. If the transverse jerk is struck at one end of the string, the disturbance will reach the other end in ______.


Speed of sound waves in a fluid depends upon ______.

  1. directty on density of the medium.
  2. square of Bulk modulus of the medium.
  3. inversly on the square root of density.
  4. directly on the square root of bulk modulus of the medium.

If c is r.m.s. speed of molecules in a gas and v is the speed of sound waves in the gas, show that c/v is constant and independent of temperature for all diatomic gases.


Two perfectly identical wires kept under tension are in unison. When the tension in the wire is increased by 1% then on sounding them together 3 beats are heard in 2 seconds. What is the frequency of each wire?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×