A wave on a string is described by $$y(x, t)=15.0 \sin (\pi x / 8-4 \pi t)$$ where $$ x $$ and $$ y $$ are in centimeters and $$ t $$ is in seconds. What is the maximum transverse speed of any point on the string?
We write the expression for the displacement in the form $$ y(x, t)=y_{m} \sin (k x-\omega t) $$
The (transverse) speed of a point on the cord is given by taking the derivative of $$ y $$
$$u(x, t)=\dfrac{\partial y}{\partial t}=-\omega y_{m} \cos (k x-\omega t)$$
The numerical coefficient of the cosine in the expression for $$ u $$ is $$ -60 \pi $$.
Thus, the maximum speed is $$ 1.88 \mathrm{m} / \mathrm{s} $$
A travelling harmonic wave on a string is described by $$ \displaystyle y(x,t)=7.5\sin \left ( 0.0050x+12t+\pi /4 \right ) $$ (a) What are the displacement and velocity of oscillation of a point at $$x = 1$$ cm and $$t = 1$$ s? Is this velocity equal to the velocity of wave propagation ? (b) Locate the points of the string which have the same transverse displacements and velocity as the $$x = 1$$ cm point at $$t = 2 s$$ , 5 s and 11s
Find the number of natural transverse vibrations of a right angled parallelepiped of volume V in the frequency interval from $$ \omega $$ to $$ \omega + d \omega $$ if the propagation velocity of vibrations is equal to $$\nu$$.
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 $$ y_{s}=4.0 \mathrm{cm}$$ . What is the transverse velocity of the string particle at $$ x=0.20 \mathrm{m} $$ at $$ t=0.50 \mathrm{s} $$.
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 $$ y_{s}=4.0 \mathrm{cm}$$ . What is the transverse velocity of the string particle at $$ x=0.20 \mathrm{m} $$ at $$ t=1.0 \mathrm{s} ? $$
The equation of a transverse wave traveling along a string is $$y=(2.0 \mathrm{mm}) \sin \left[\left(20 \mathrm{m}^{-1}\right) x-\left(600 \mathrm{s}^{-1}\right) t\right]$$ Find the maximum transverse speed of a particle in the string.
A standing wave results from the sum of two transverse traveling waves given by $$y_{1}=0.050 \cos (\pi x-4 \pi t)$$ and $$y_{2}=0.050 \cos (\pi x+4 \pi t)$$ where $$ x, y_{1}, $$ and $$ y_{2} $$ are in meters and $$ t $$ is in seconds. what is the value of the first time the particle at $$ x=0 $$ has zero velocity?
A standing wave results from the sum of two transverse traveling waves given by $$y_{1}=0.050 \cos (\pi x-4 \pi t)$$ and $$y_{2}=0.050 \cos (\pi x+4 \pi t)$$ where $$ x, y_{1}, $$ and $$ y_{2} $$ are in meters and $$ t $$ is in seconds. what is the value of the second time the particle at $$ x=0 $$ has zero velocity?
A standing wave results from the sum of two transverse traveling waves given by $$y_{1}=0.050 \cos (\pi x-4 \pi t)$$ and $$y_{2}=0.050 \cos (\pi x+4 \pi t)$$ where $$ x, y_{1}, $$ and $$ y_{2} $$ are in meters and $$ t $$ is in seconds. what is the value of the third time the particle at $$ x=0 $$ has zero velocity?
A wave on a string is described by $$y(x, t)=15.0 \sin (\pi x / 8-4 \pi t)$$ where $$ x $$ and $$ y $$ are in centimeters and $$ t $$ is in seconds. What is the transverse speed for a point on the string at $$ x=6.00 \mathrm{cm} $$ when $$ t=0.250 \mathrm{s} ? $$
Frequency of wave is $$6\times 10^{15}Hz$$. The wave is