Umakant Kondapure, Collin Fernandes, Nipun Bhatia, Vikram Bathula and, Ketki Deshpande Solutions for Chapter: Wave Motion, Exercise 3: Competitive Thinking

The phase difference between two particles in a medium separated by a distance $x$ is $\frac{\pi }{6}.$ If the frequency of the oscillation is $50 \mathrm{Hz}$ and the velocity of propagation of the wave is $100 \mathrm{m} {\mathrm{s}}^{-1},$ then $\mathrm{x}=$

If the maximum particle velocity is $4$times of the wave velocity then relation between wavelength and amplitude is

If $y_1=a\sin \left(2000\pi t\right)$ and $y_2=a\sin \left(2008\pi t\right)$ then number of beats produced per second are 

A wave travelling along the $x-$axis is described by the equation $y(x,t)=0.005\cos (\alpha x-\beta t).$ If the wavelength and the time period of the wave are $0.08 \mathrm{m}$ and $2.0 \mathrm{s}$, respectively, then $\alpha$ and $\beta$ in appropriate units are 

The frequency of tuning forks $A$ and $B$ are respectively $3\%$ more and $2\%$ less than the frequency of tuning fork $C$. When $A$ and $B$ are simultaneously excited, $5$ $\mathrm{beats} \mathrm{per} \mathrm{second}$ are produced. Then the frequency of the tuning fork '$A$' (in $\mathrm{Hz}$) is

A motorcycle starts from rest and accelerates along a straight path at $2 \mathrm{m} {\mathrm{s}}^{-2}$. At the starting point of the motorcycle, there is a stationary electric siren. How far has the motorcycle gone when the driver hears the frequency of the siren at $94\%$ of its value when the motorcycle was at rest? ($\mathrm{speed} \mathrm{of} \mathrm{sound}$ $=330{\mathrm{ms}}^{-1}$) 

Two sources $A$ and $B$ are sending notes of frequency $680 \mathrm{Hz}$. A listener moves from $A$to $B$ with a constant velocity $u$. If the speed of sound in air is $340{\mathrm{ms}}^{-1},$ what must be the value of $u$ so, that he hears $10 \mathrm{beats} \mathrm{per} \mathrm{seconds}$ 

A person speaking normally produces a sound intensity of $40 \mathrm{dB}$ at a distance of $1 \mathrm{m}$. If the threshold intensity for reasonable audibility is $20 \mathrm{dB},$ the maximum distance at which he can be heard clearly is