Umakant Kondapure, Collin Fernandes, Nipun Bhatia, Vikram Bathula and, Ketki Deshpande Solutions for Chapter: Wave Motion, Exercise 2: Critical Thinking

A wave is expressed by the equation, $y=0.5\sin \left[\pi \right(0.01x-3t\left)\right]$, where $y$ and $x$ are in $\mathrm{metre}$ and $t$ is in $\mathrm{second}$. The speed of propagation of the wave is,

Two sources of sound $A$ and $B$ produce a wave of $350 \mathrm{Hz}$. They vibrate in the same phase. The particle $P$ is vibrating under the influence of these two waves. If the amplitudes at the point $P$ produced by the two waves is $0.3 \mathrm{mm}$ and $0.4 \mathrm{mm}$, then the resultant amplitude of the point $P$ will be [given, $AP-BP=25 \mathrm{cm}$ and the velocity of sound is $350 \mathrm{m} {\mathrm{s}}^{-1}$],

A tuning fork whose frequency is given by the manufacturer as $512\mathrm{Hz}$ is being tested using an accurate oscillator. It is found that they produce $2 \mathrm{beats} \mathrm{per} \mathrm{second}$ when the oscillator reads $514 \mathrm{Hz}$ and $6 \mathrm{beats} \mathrm{per} \mathrm{second}$ when it reads $510 \mathrm{Hz}$. The actual frequency of the fork is,

Two sounding bodies producing progressive waves given by, $y_1=4\sin \left(400\pi t\right)$ and ${\mathrm{y}}_2=3\sin \left(404\pi \mathrm{t}\right)$, are situated very near to the ears of a person. He will hear (here, intensity ratio is between maxima and minima),

A source of sound emitting a note of frequency $90 \mathrm{Hz}$ moves towards an observer with speed equal to ${\left(\frac{1}{10}\right)}^{\text{th }}$ of velocity of sound. The frequency of the note heard by the observer will be,

A train has just completed a U-curve in a track which is a semi-circle. The engine is at the forward end of the semi circular part of the track while the last carriage is at the rear end of the semicircular track. The driver blows a whistle of frequency $200 \mathrm{Hz}$. The velocity of sound is $340 \mathrm{m} {\mathrm{s}}^{-1}$. Then, the apparent frequency as observed by a passenger in the middle of a train when the speed of the train is $30 \mathrm{m} {\mathrm{s}}^{-1}$ is,

Assertion: On reflection from a rigid boundary (denser medium), there is a complete reversal of phase.

Reason: This is because, on reflection at a denser medium, both the particle velocity and wave velocity are reversed in sign.

A sound source emits sound waves in a uniform medium. If energy density is $E$ and maximum speed of the particles of the medium is $v_{\text{max}}$, the plot between $E$ and $v_{\max }$ is best represented by,