Tag: speed and acceleration of travelling wave

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Questions Related to speed and acceleration of travelling wave

Multiple choice physics wave motion wave velocity speed and acceleration of travelling wave speed of a travelling wave

A rope of length $L$ and mass $m$ hangs freely from the celling. The velocity of transverse wave as a furcion position $x$ along the rope is proportional to

  1. $x ^ { 0 }$

  2. $\sqrt { x }$

  3. $\frac { 1 } { \sqrt { x } }$

  4. $x$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Tension at distance x from the free end is T = mu * g * x. Wave speed v = sqrt(T / mu) = sqrt(g * x). Thus, v is proportional to sqrt(x).

Multiple choice physics wave motion wave velocity speed and acceleration of travelling wave speed of a travelling wave

If a string is stretched by $\dfrac{L}{20}$ then velocity of wave is $V$. When string is stretched by $\dfrac{L}{10}$ then velocity becomes

  1. $\dfrac{V}{\sqrt 2}$

  2. $V$

  3. $2V$

  4. $\sqrt 2 V$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

For a stretched string, T = Y * A * (delta_L / L). Wave speed v = sqrt(T / mu) = sqrt(Y * A * delta_L / (L * mu)). Since v is proportional to sqrt(delta_L), doubling the extension delta_L (from L/20 to L/10) increases the velocity by a factor of sqrt(2).

Multiple choice physics wave motion wave velocity speed and acceleration of travelling wave speed of a travelling wave

Sinusoidal waves 5.00 cm in amplitude are to be transmitted along a string having a linear mass density equal to 4.00 * $10^-2 kg/m$. If the source can deliver a average power of 90 W and the string is under a tension of 100 N,then the highest frequency at which the source can operate is (take $\pi^2 = 10)$:

  1. 45 Hz

  2. 50 Hz

  3. 30 Hz

  4. 62 Hz
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Average power P = 2 * pi^2 * f^2 * A^2 * mu * v. Tension T = 100 N, mu = 0.04 kg/m, so v = sqrt(100 / 0.04) = 50 m/s. P = 90 W, A = 0.05 m. 90 = 2 * 10 * f^2 * (0.05)^2 * 0.04 * 50. 90 = 20 * f^2 * 0.0025 * 2 = 0.1 * f^2. f^2 = 900, so f = 30 Hz.

Multiple choice physics wave motion wave velocity speed and acceleration of travelling wave speed of a travelling wave

The equation of a stationary wave in a string is y =(4) sin[($3.14m^-1$)x] cos ${\omega}t$. (mm)
Select the correct alternative(s).

  1. the amplitude of component waves is 2 mm

  2. the amplitude of component waves is 4 mm

  3. the smallest possible length of string is 0.5 m

  4. the smallest possible length of string is 1.0 m
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The equation of stationary wave in a string is the amplitude of component waves is $4$mm.

Hence, option $B$ is correct ansnwer.

Multiple choice physics wave motion wave velocity speed and acceleration of travelling wave speed of a travelling wave

A wave represented by a given equation $y (x,t) = a \sin (\omega t - kx)$superimposes on another wave giving a stationary wave having antinode at $x = 0 $ then the equation of the another wave is 

  1. $y = - a \sin (\omega t - kx)$

  2. $y = a \sin (\omega t + kx)$

  3. $y = - a \sin (\omega t + kx)$

  4. $y = - a \cos (\omega t + kx)$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$\begin{array}{l} a\sin  \left( { wt-kx } \right) +{ y _{ 1 } }=2a\sin  \cot  \cos  kx \ \Rightarrow y=a\sin  \left( { wt+kx } \right)  \ Ans.\, \, (B) \end{array}$

Multiple choice physics wave motion wave velocity speed and acceleration of travelling wave speed of a travelling wave

A travelling wave passes  point of observation. At this point, the time interval between successive crests is $0.2\, s$ and 

  1. The wavelength is $5\, m$

  2. The frequency is $5\, Hz$

  3. The velocity of propagation is $5\, m/s$

  4. The wavelength is $0.2\, m$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$\begin{array}{l} Accorrding\, \, to\, \, question....................... \ Here, \ Difference\, between\, two\, successive\, crest\, is\, 2p. \ passes\, difference\, (\Delta \varphi )=\frac { { 2\pi  } }{ T }  \ \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, T=time\, { { int } }erval(\Delta t) \ \therefore \, \, \, n=2\pi =\frac { { 2\pi  } }{ T } \times 0.2 \ \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \Rightarrow \frac { 1 }{ T } =5{ \sec ^{ -1 }  } \ \Rightarrow n=5Hz \ So\, the\, correct\, option\, is\, B. \end{array}$

Multiple choice physics wave motion wave velocity speed and acceleration of travelling wave speed of a travelling wave

The equation of standing wave in a stretched string is given by by y = 5sin($\frac{{\pi}{x}} {3}$) cos $(40{\pi}t)$, where x and y are in cm and t in second. The separation between two consecutive nodes is (in cm) 

  1. 1.5

  2. 3

  3. 6

  4. 4
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$\begin{array}{l} y=5\sin  \left( { \frac { { \pi x } }{ 3 }  } \right) .\cos  \left( { 4\pi t } \right)  \ Here\, in\, above\, equation\, \, k=\frac { \pi  }{ 3 }  \ \frac { { 2\pi  } }{ \lambda  } =\frac { \pi  }{ 3 }  \ \lambda =6cm \ Hence,\, dis\tan  ce\, between\, 2\, nodes\, is\, \frac { \lambda  }{ 2 } =3cm \end{array}$

Hence, the option $B$ is the correct answer.

Multiple choice physics wave motion wave velocity speed and acceleration of travelling wave speed of a travelling wave

The equation of a wave travelling on a string is $y=4 sin \left[ \dfrac { \pi  }{ 2 } \left( 8t-\dfrac { x }{ 8 }  \right)  \right] $, where $x,y$ are in cm and $t$ is in second. The velocity of the wave is

  1. $64 cm/s$ in $-x$ direction

  2. $32 cm/s$ in $-x-$ direction

  3. $32 cm/s$ in $+x-$ direction

  4. $64 cm/s$ in $+x-$ direction
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The equation is y = 4 sin(4 * pi * t - pi * x / 16). Comparing to y = A sin(omega * t - k * x), omega = 4 * pi and k = pi / 16. Wave speed v = omega / k = 4 * pi / (pi / 16) = 64 cm/s. Since the signs of omega * t and k * x are opposite, the wave travels in the +x direction.

Multiple choice physics wave motion wave velocity speed and acceleration of travelling wave speed of a travelling wave

Two travelling waves $y _1=A sin[k(x-ct)]$ and $y _2\, sin[k(x+ct)]$ are superimposed on string. The distance between adjacent nodes is 

  1. $c\, t/\pi$

  2. $c\, t/2\pi$

  3. $\pi/2k$

  4. $\pi/k$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The superposition of two waves traveling in opposite directions forms a standing wave. The distance between adjacent nodes is lambda / 2. Since k = 2 * pi / lambda, lambda / 2 = pi / k.