A wave is represented by the equation$y = 7\sin \left( {7\pi t - 0.04\,x\pi + \frac{\pi }{3}} \right)$ $x$ is in metres and $ t$ is in seconds. The speed of the wave is
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A police van, moving at $22\, m/s$ , chases a motor-cyclist. The police man sounds horn at $176\, Hz$ , while both of them move towards a stationary siren of frequency $165\, Hz$ as shown in the figure. If the motor-cyclist does not observe any beats, his speed must be .... $m/s$ (take the speed of sound $= 330\, m/s$ )
A student is performing the experiment of Resonance Column. The diameter of the column tube is $4$ $cm$. The frequency of the tuning fork is $512$ $Hz$. The air temperature is $38^o C$ in which the speed of sound is $336$ $m/s$. The zero of the meter scale coincides with the top end of the Resonance column tube. When the first resonance occurs, the reading of the water level in the column is ..... $cm$
A sonometer wire oflength $1.5\ m$ is made of steel. The tension in it produces an elastic strain of $1 \%$. What is the fundamental frequency of steel if density and elasticity of steel are $7.7 \times 10^3 $ $kg/m^3$ and $2.2 \times 10^{11}$ $N/m^2$ respectively?
In stationary waves, distance between a node and its nearest antinode is $20 cm$. The phase difference between two particles having a separation of $60 cm$ will be
One end of a string of length $L$ is tied to the ceiling of a lift accelerating upwards with an acceleration $2g$. The other end of the string is free. The linear mass density of the string varies linearly from $0$ to $\lambda$ from bottom to top.
A uniform string resonates with a tuning fork, at a maximum tension of $32 \,N$. If it is divided into two segments by placing a wedge at a distance one-fourth of length from one end, then to resonance with same frequency the maximum value of tension for string will be ........... $N$
The equation of stationary wave along a stretched string is given by $y = 5\sin \frac{{\pi x}}{3}\cos 40\pi t$, where $x $ and $y$ are in $cm$ and $t$ in second. The separation between two adjacent nodes is..... $cm$
A transverse wave is represented by $y= Asin $ $\left( {\omega t - kx} \right)$. For what value of the wavelength is the wave velocity equal to the maximum particle velocity ?
In Melde's experiment, the string vibrates in $4$ loops when a $50 \,gram$ weight is placed in the pan of weight $15\, gram.$ To make the string to vibrates in $6$ loops the weight that has to be removed from the pan is