The equation of travelling wave is $y=a \sin 2 \pi\left(p t-\frac{x}{5}\right)$. Then the ratio of maximum particle velocity to wave velocity is ...........
Easy
Download our app for free and get started
(c)
Equation of travelling wave
$y=a \sin 2 \pi\left(p t-\frac{x}{5}\right)$
Maximum particle velocity $\left(v_y\right)=A \omega$ or $v_y=a \times 2 \pi p$
Wave velocity $(v)=\frac{\omega}{k}=\frac{2 \pi p}{2 \pi / 5}=5 p$
$\therefore \frac{v_y}{v}=\frac{2 \pi a}{5}$
Download our appand get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Similar Questions
- 1An earthquake generates both transverse $(S)$ and longitudinal $(P)$ sound waves in the earth. The speed of $S$ waves is about $4.5 \,km/s$ and that of $P$ waves is about $8.0 \,km/s.$ A seismograph records $P$ and $S$ waves from an earthquake. The first $P$ wave arrives $4.0\, min$ before the first $S$ wave. The epicenter of the earthquake is located at a distance about .... $km$View Solution
- 2The ratio of maximum to minimum intensity due to superposition of two waves is $\frac{{49}}{9}$ Then the ratio of the intensity of component waves is .View Solution
- 3A vibrating string of certain length $l$ under a tension $T$ reasonates with a mode corresponding to the first overtone (third harmonic) of an air column of length $75$ $cm$ inside a tube closed at one end. The string also generates $4$ beats per second when excited along with a tuning fork of frequency $n$. Now when the tension of the string is slightly increased the number of beats reduces to $2$ per second. Assuming the velocity of sound in air to be $340$ $m/s$, the frequency $n$ of the tuning fork in $Hz $ isView Solution
- 4A progressive wave travelling in positive by $x-$ direction given by $y = a\, sin (kx -\omega t)$ meets fixed end at $x = 0$. The reflected wave may be given byView Solution
- 5View SolutionDoppler's effect will not be applicable when the velocity of sound source is
- 6In a resonance tube the first resonance with a tuning fork occurs at $16 cm$ and second at $49 cm.$ If the velocity of sound is $330 m/s,$ the frequency of tuning fork isView Solution
- 7The relation between frequency $‘n’$ wavelength ‘$\lambda$’ and velocity of propagation $‘v’$ of wave isView Solution
- 8A wave equation is $y = 10^{-4}\, sin\, (60 t + 2x)$ Where $x$ and $y$ are in $metres$ and $t$ is in $sec$ . Which of the following statements is correct ?View Solution
- 9A transverse harmonic wave on a string is given by $y(x, t)=5 \sin (6 t+0.003 x)$ where $x$ and $y$ are in $cm$ and $t$ in $sec$. The wave velocity is $...........\,ms ^{-1}$.View Solution
- 10The wave described by $y=0.25 \,sin\left[ {10\pi x - 2\pi t} \right]$, where $x$ and $y$ are in meters and $t$ in seconds, is a wave travelling along theView Solution