Physical World
A particle performing S.H.M. starts from equilibrium position and its time period is $$16$$ second. After $$2$$ seconds its velocity is $$\pi \ m/s$$. Amplitude of oscillation is $$(\cos 45^{\circ} = \dfrac {1}{\sqrt {2}})$$
A certain loudspeaker system emits sound isotropically with a frequency of $$ 2000 \mathrm{Hz} $$ and an intensity of $$ 0.960 \mathrm{mW} / \mathrm{m}^{2} $$ at distance of $$ 6.10 \mathrm{m} $$. Assume that there are no reflections.what are the displacement amplitude ?
The source being isotropic means $$ A_{\text {sphere }}=4 \pi r^{2} $$ is used in the intensity definition
$$ I= P / A, $$ which further implies
$$\dfrac{I_{2}}{I_{1}}=\dfrac{P / 4 \pi r_{2}^{2}}{P / 4 \pi r_{1}^{2}}=\left(\dfrac{r_1}{r_{2}}\right)^{2}$$
with $$ I_{1}=9.60 \times 10^{-4} \mathrm{W} / \mathrm{m}^{2}, \omega=2 \pi(2000 \mathrm{Hz}), \mathrm{V}$$
$$=343 \mathrm{m} / \mathrm{s}, $$ and $$ \rho= 1.21 \mathrm{kg} / \mathrm{m}^{3}, $$ we obtain
$$s_{m}=\sqrt{\dfrac{2 I}{\rho v \omega^{2}}}=1.71 \times 10^{-7} \mathrm{m}$$
A particle performing S.H.M. starts from equilibrium position and its time period is $$16$$ second. After $$2$$ seconds its velocity is $$\pi \ m/s$$. Amplitude of oscillation is $$(\cos 45^{\circ} = \dfrac {1}{\sqrt {2}})$$
The displacement of a particle executing simple harmonic motion is given by $$x = 3 sin [2 \pi t + \frac{\pi}{4}]$$ where x is in metres and t is in seconds. The amplitude and maximum speed of the particle is:
A particle executes SHM of period $$12$$s. After two seconds, it passes through the centre of oscillation, the velocity is found to be $$3.142 cm s^{-1}$$. The amplitude of oscillation is:
The equation of a wave is given by $$y= 10$$ sin$$\left(\dfrac{2\pi}{45} t + \alpha \right)$$. If the displacement is $$5 cm$$ at $$t=0$$, the the total phase at $$t=7.5 s$$ is
For a particular transverse standing wave on a long string, one of the antinodes is at $$ x=0 $$ and an adjacent node is at $$ x=0.10 \mathrm{m} . $$ The displacement $$ y(t) $$ of the string particle at $$ x=0 $$ is shown in Fig. $$ 16-40 $$ where the scale of the $$ y $$ axis is set by $$ y_{s}=4.0 \mathrm{cm} . $$ When $$ t=0.50 \mathrm{s}, $$ what is the displacement of the string particle at $$ x=0.20 \mathrm{m} $$
For a particular transverse standing wave on a long string, one of the antinodes is at $$ x=0 $$ and an adjacent node is at $$ x=0.10 \mathrm{m} . $$ The displacement $$ y(t) $$ of the string particle at $$ x=0 $$ is shown in Fig. $$ 16-40 $$ where the scale of the $$ y $$ axis is set by $$ y_{s}=4.0 \mathrm{cm} . $$ When $$ t=0.50 \mathrm{s}, $$ what is the displacement of the string particle at $$ x=0.30 \mathrm{m} ? $$
A single pulse, given by $$ h(x-5.0 t), $$ is shown in Fig. $$ 16-45 $$ for $$ t=0 . $$ The scale of the vertical axis is set by $$ h_{s}=2 . $$ Here $$ x $$ is in centimeters and $$ t $$ is in seconds.Plot $$ h(x-5 t) $$ as a function of $$ x $$ for $$ t=2 \mathrm{s} $$
A single pulse, given by $$ h(x-5.0 t), $$ is shown in Fig. $$ 16-45 $$ for $$ t=0 . $$ The scale of the vertical axis is set by $$ h_{s}=2 . $$ Here $$ x $$ is in centimeters and $$ t $$ is in seconds.Plot $$ h(x-5 t) $$ as a function of $$ t $$ for $$ x=10 \mathrm{cm} $$
Two sinusoidal& 120Hz waves, of the same frequency and amplitude, are to be sent in the positive direction of an $$ x $$ axis that is directed along a cord under tension. The waves can be sent in phase, or they can be phase-shifted. Figure $$ 16-47 $$ shows the amplitude $$ y^{\prime} $$ of the resulting wave versus the distance of the shift (how far one wave is shifted from the other wave). The scale of the vertical axis is set by $$ y_{s}^{\prime}=6.0 \mathrm{mm} . $$ If the equations for the two waves are of the form $$ y(x, t)=y_{m} \sin (k x \pm \omega t), $$ what is $$ y_{m}$$
If amplitude of waves at distance r from a point source is A, the amplitude at a distance 2r will be