Sound Wave:Displacement Equation

Q.

A traveling wave in a stretched string is described by the equation;

y = A sin (kx- $\omega$t). The maximum particle velocity is :

1. A $\omega$

2. $\frac{\omega }{k}$

3. $\frac{d\omega }{dk}$

4. $\frac{x}{\omega }$

Q. The displacement equation of a travelling sound wave along $x$ axis is given by $s=5\times {10}^{-5}\sin (500t-2x)$, where $s$ and $x$ are in meters and $t$ in seconds. Choose the correct option(s) among the following.

1. Ratio of displacement amplitude of the particles to the wavelength of wave is $1.1\times {10}^{-5}$.
2. Ratio of displacement amplitude of the particles to the wavelength of wave is $1.59\times {10}^{-5}$.
3. Ratio of the velocity amplitude of the particles to the wave speed is $2\times {10}^{-4}$.
4. Ratio of the velocity amplitude of the particles to the wave speed is ${10}^{-4}$.

Q.

A wave is represented by the equation

y = (0.001 mm) sin[(50 $s^{-1}$)t + (2.0 $m^{-1}$)x].

1. The wave velocity = 100 m/s.

2. The wavelength = 2.0 m.

3. The frequency = $\frac{25}{\pi }$ Hz.

4. The amplitude = 0.01 mm.

Q. The displacement equation of a travelling sound wave along $x$ axis is given by $s=5\times {10}^{-5}\sin (500t-2x)$, where $s$ and $x$ are in meters and $t$ in seconds. Choose the correct option(s) among the following.

1. Ratio of displacement amplitude of the particles to the wavelength of wave is $1.1\times {10}^{-5}$.
2. Ratio of displacement amplitude of the particles to the wavelength of wave is $1.59\times {10}^{-5}$.
3. Ratio of the velocity amplitude of the particles to the wave speed is $2\times {10}^{-4}$.
4. Ratio of the velocity amplitude of the particles to the wave speed is ${10}^{-4}$.