Question \( / \) Answered step-by-step as shown in figure, then mark correct... statements. (a) ^ ll particles in between \( \wedge \) string fixed at both ends is vibrating as shown in figure, then mark correct statements. (a) \( \wedge \) II particles in between \( x \) and \( { }_{y} \) are vibrating in phase (b) \( { }_{\Lambda} \| \) particles in belween \( { }_{A} \) and \( { }_{x} \) are vibrating in phase with paricles between \( x \) and \( y \) (c) \( { }_{\triangle} \) Il particles between \( { }_{A} \) and \( { }_{X} \) are vibrating in phasc with particles in \( y \) and \( { }_{B} \) (d) \( \wedge \| \) particles of string are in phase
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The displacement associated with a standing wave on a sonometer is given by the following equation: $$y(x, t)=2 a \sin \left(\frac{2 \pi}{\lambda} x\right) \cos 2 \pi v$$ If the length of the string is $L$ then the allowed values of $\lambda$ are $2 L, 2 L / 2,2 L / 3, \ldots$ (see Sec. 13.2). Consider the case when $\lambda=2 L / 5$; study the time variation of displacement in each loop and show that alternate loops vibrate in phase (with different points in a loop having different amplitudes) and adjacent loops vibrate out of phase.
A stretched string is given simultaneous displacement in the $x-$ and $y-$ directions such that $$x(z, t)=a \cos \left(\frac{2 \pi}{\lambda} z-2 \pi v t\right)$$ and $$y(z, t)=a \cos \left(\frac{2 \pi}{\lambda} z-2 \pi v t\right)$$ Show that the string will vibrate along a direction making an angle $\pi / 4$ with the $x$ and $y$ axes.
Refer to the wave in the string described in Exercise 37 of Section $10.3 .$ For a point on the string, the displacement $y$ is given by $y=A \sin 2 \pi\left(\frac{t}{T}-\frac{x}{\lambda}\right) .$ We see that each point on the string moves with simple harmonic motion. Sketch two cycles of y as a function of t for the given values. $A=0.350$ in. $T=0.250 \mathrm{s}, \lambda=24.0 \mathrm{in} ., x=20.0 \mathrm{in}$.
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