Tag: standing waves in strings

Questions Related to standing waves in strings

The equation of a stationary wave is given by $ y= 5cos \frac { \pi x }{ 3 }  sin 40 \pi t $. where y and x are given cm and time t in second then the amplitude of the progressive wave is

physics stationary waves formation of stationary waves stationary waves and its graphical representation standing waves in strings from moving to stationary stationary (or standing) waves

  1. $2.5 cm$

  2. $10 cm$

  3. $5 cm$

  4. $7.5 cm$

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Correct Option: A

The equation of progressive wave travelling along positive direction of x-axis having an amplitude of $0.04\ m$, frequency $440\ Hz$ and wave velocity $330 m/s$ is

physics stationary waves formation of stationary waves stationary waves and its graphical representation standing waves in strings from moving to stationary stationary (or standing) waves

  1. $y = 0.04\sin 2\pi \left (440t - \dfrac {4x}{3}\right )$

  2. $y = 0.04\cos 2\pi \left (440t - \dfrac {3x}{4}\right )$

  3. $y = 0.04\sin 2\pi \left (440t + \dfrac {4x}{3}\right )$

  4. $y = 0.04\cos 2\pi \left (440t + \dfrac {4x}{3}\right )$

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Correct Option: C

In a stationary wave

physics stationary waves formation of stationary waves stationary waves and its graphical representation standing waves in strings from moving to stationary stationary (or standing) waves

  1. Strain is maximum at nodes

  2. amplitude is minimum at nodes

  3. Strain is maximum at antinodes

  4. Amplitude is zero at all points

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Correct Option: B

The frequency of plane progressive wave is $100$ Hz. After how much time the same point will be $90^o$ out of phase?

physics stationary waves formation of stationary waves stationary waves and its graphical representation standing waves in strings from moving to stationary stationary (or standing) waves

  1. $2.5\times 0^{-3}s$.

  2. $3.5\times 0^{-3}s$.

  3. $4.5\times 0^{-3}s$.

  4. $5.5\times 0^{-3}s$.

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Correct Option: A
Explanation:

$w=2\Pi f$

where f is frequency of wave
Phase angle, $\theta wt$
$90^{\circ}=2\Pi ft$

$t=\dfrac{\Pi }{2\times 2\Pi f}$

$t=\dfrac{1}{4\times 100} $sec

$t=2.5\times 10^{-3}$ sec

Progressive wave are waves originating from a source such that they never return to the source.

physics stationary waves formation of stationary waves stationary waves and its graphical representation standing waves in strings from moving to stationary stationary (or standing) waves

  1. True

  2. False

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Correct Option: A
Explanation:

progressive waves are waves after generation from the source the keep on propagating on the direction of propagation .

so the answer is A.

The equation, $Y=0.02 sin (500 \pi t) cos(4.5x)$ represents

physics stationary waves formation of stationary waves stationary waves and its graphical representation standing waves in strings from moving to stationary stationary (or standing) waves

  1. progressive wave of frequency 250 Hz along x-axis

  2. a stationary wave of wavelength 1.4 m

  3. a transverse progressive wave of amplitude 0.02 m

  4. progressive wave of speed of about $350ms^{-1} $

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Correct Option: B
Explanation:

Comparing the given wave equation with standard standing wave equation
$y (x, t) = A \sin (\omega t)\cos (kx)$, 


we get, $k =4.5$

$k = \dfrac{2\pi}{\lambda}$

$\Rightarrow \lambda = \dfrac{2\pi}{k} =1.4$ $m$

The equation of a progressive wave is $y=4\,sin(4\pi t-0.04x+\dfrac{\pi}{3})$ where x is in metre and t is in second. The velocity of the wave is

physics stationary waves formation of stationary waves stationary waves and its graphical representation standing waves in strings from moving to stationary stationary (or standing) waves

  1. $100\pi\,m/s$

  2. $50\pi\,m/s$

  3. $25\pi\,m/s$

  4. $\pi\,m/s$

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Correct Option: A
Explanation:

The equation of the progressive wave is given as, $y=4\,sin(4\pi t-0.04x+\dfrac{\pi}{3})$.

The velocity of the wave would be equal to

$\dfrac{\omega}{k}=\dfrac{4\pi}{0.04}=100\pi\;m/s$

Which of the following statements are correct?

physics stationary waves formation of stationary waves stationary waves and its graphical representation standing waves in strings from moving to stationary stationary (or standing) waves

  1. A wave front is a locus of points vibratig in same phase

  2. Wavelength is separation between two consecutive points vibrating in same phase

  3. For two sources to be coherent their frequencies must be same

  4. All of the above statements are correct.

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Correct Option: D

A string is under tension so that its length is increased by $1/n$ times its original length. The ratio of fundamental frequency of longitudinal vibrations and transverse vibrations will be

physics oscillations and waves standing waves in strings standing waves reflection of waves

  1. $1:n$

  2. ${n}^{2}:1$

  3. $\sqrt{n}:1$

  4. $n:n+1$

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Correct Option: D

Motion that moves to and fro in regular time intervals is called _________________ motion.

physics oscillations and waves standing waves in strings standing waves reflection of waves

  1. Vibratory

  2. Translatory

  3. Rotatory

  4. Accelerating

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Correct Option: A
Explanation:

Sounds are made by vibrations. Some vibrations are easy to see. The vibrations that create sound must travel through a medium, such as air or water, or anything made of molecules. With each forward motion, air molecules pulse outward, pushing other air molecules and crowding them together. With each backward motion, the molecules get less crowded. The forward and backward vibration of the glass creates a chain reaction of crowded and not-so-crowded molecules that ripples through the air. This traveling vibration is called a sound wave. 
Motion that moves to and fro in regular time intervals is called vibratory or oscillatory motion.