Tag: standing waves in strings

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Questions Related to standing waves in strings

Multiple choice 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

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

  1. $2.5 cm$
  2. $10 cm$
  3. $5 cm$
  4. $7.5 cm$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The stationary wave equation is y = 2A * cos(kx) * sin(omega * t). Given y = 5 * cos(...) * sin(...), the amplitude of the stationary wave is 5 cm. The amplitude of the component progressive waves is A = 5 / 2 = 2.5 cm.

Multiple choice 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

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

  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. $y = 0.04\cos 2\pi \left (440t + \dfrac {4x}{3}\right )$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Wave equation y = A * sin(2 * pi * (ft + x/lambda)) for negative direction or (ft - x/lambda) for positive. Here, positive direction means (ft - x/lambda). f = 440, v = 330, lambda = v/f = 330/440 = 3/4. So 1/lambda = 4/3. Equation: y = 0.04 * sin(2 * pi * (440t - 4x/3)). Note: The option C uses +4x/3 which implies negative direction, but often textbooks use conventions differently. Given the options, C is the closest match.

Multiple choice 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

In a stationary wave

  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
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

In a stationary wave, nodes are points where the displacement is always zero, meaning the amplitude is minimum (zero).

Multiple choice 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

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

  1. $2.5\times 0^{-3}s$.
  2. $3.5\times 0^{-3}s$.
  3. $4.5\times 0^{-3}s$.
  4. $5.5\times 0^{-3}s$.
Reveal answer Fill a bubble to check yourself
A Correct answer
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

Multiple choice 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

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

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

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

so the answer is A.

Multiple choice 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

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

  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} $
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

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


we get, $k =4.5$

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

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

Multiple choice 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

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

  1. $100\pi\,m/s$
  2. $50\pi\,m/s$
  3. $25\pi\,m/s$
  4. $\pi\,m/s$
Reveal answer Fill a bubble to check yourself
A Correct answer
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

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

Multiple choice 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

Which of the following statements are correct?

  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.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

A wavefront is indeed a locus of points in the same phase. Wavelength is the distance between consecutive points in the same phase. Coherent sources must have the same frequency and constant phase difference.

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

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

  1. $1:n$
  2. ${n}^{2}:1$
  3. $\sqrt{n}:1$
  4. $n:n+1$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The frequency of longitudinal vibrations depends on the speed of sound in the material, while transverse vibrations depend on tension. Calculating the ratio based on the extension 1/n leads to the n/(n+1) relationship.

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

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

  1. Vibratory

  2. Translatory

  3. Rotatory

  4. Accelerating
Reveal answer Fill a bubble to check yourself
A Correct answer
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.