(D) Given: Velocity $v = 10\,m/s$,Frequency $f = 100\,Hz$,Path difference $\Delta x = 2.5\,cm = 0.025\,m$.First,calculate the wavelength $\lambda$ usi

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(D) Given: Velocity $v = 10\,m/s$,Frequency $f = 100\,Hz$,Path difference $\Delta x = 2.5\,cm = 0.025\,m$.First,calculate the wavelength $\lambda$ using the relation $v = f\lambda$:$\lambda = \frac{v}{f} = \frac{10}{100} = 0.1\,m = 10\,cm$.Now,use the formula for phase difference $\Delta \phi$:$\Delta \phi = \frac{2\pi}{\lambda} \times \Delta x$.Substituting the values:$\Delta \phi = \frac{2\pi}{10\,cm} \times 2.5\,cm = \frac{2\pi}{4} = \frac{\pi}{2}$ radians.

Class 11 Physics Waves and Sound Wave Equation and Characteristics of Waves

Medium

$A$ transverse progressive wave on a stretched string has a velocity of $10\,m/s$ and a frequency of $100\,Hz$. The phase difference between two particles of the string which are $2.5\,cm$ apart will be:

A
$\frac{\pi}{8}$
B
$\frac{\pi}{4}$
C
$\frac{3\pi}{8}$
D
$\frac{\pi}{2}$

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Waves and Sound

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Wave Equation and Characteristics of Waves

$A$ transverse wave is described by the equation $y = A \sin [2\pi (f t - x/\lambda ) ]$. The maximum particle velocity is equal to four times the wave velocity if:

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What is a wave equation?

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$A$ wave equation is $y = 10^{-4} \sin(60t + 2x)$,where $x$ and $y$ are in $m$ and $t$ is in $s$. Which of the following statements is correct?

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The figure represents the instantaneous picture of a longitudinal harmonic wave travelling along the negative $x$-axis. Identify the correct statement$(s)$ related to the movement of the points shown in the figure. The points with maximum displacement are:

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$A$ transverse harmonic wave on a string is given by $y(x, t) = 5 \sin (6t + 0.003x)$,where $x$ and $y$ are in $cm$ and $t$ is in $s$. The wave velocity is $...........\,ms^{-1}$.

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$A$ transverse progressive wave on a stretched string has a velocity of $10\,m/s$ and a frequency of $100\,Hz$. The phase difference between two particles of the string which are $2.5\,cm$ apart will be:

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$A$ transverse wave is described by the equation $y = A \sin [2\pi (f t - x/\lambda ) ]$. The maximum particle velocity is equal to four times the wave velocity if:

What is a wave equation?

$A$ wave equation is $y = 10^{-4} \sin(60t + 2x)$,where $x$ and $y$ are in $m$ and $t$ is in $s$. Which of the following statements is correct?

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$A$ transverse harmonic wave on a string is given by $y(x, t) = 5 \sin (6t + 0.003x)$,where $x$ and $y$ are in $cm$ and $t$ is in $s$. The wave velocity is $...........\,ms^{-1}$.

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