Waves

Which one of the following options correctly represents a thermodynamic process that is used as a correction in the determination of the speed of sound in an ideal gas?

An observer is moving with half the speed of light towards a stationary microwave source emitting waves at frequency 10 GHz. What is the frequency of the microwave measured by the observer ? (speed of light = $3\times10^8$ ms$^{-1}$)

Two wires $W_1$ and $W_2$ have the same radius r and respective densities $\rho_1$ and $\rho_2$ such that $\rho_2=4\rho_1$. They are joined together at the point O, as shown in the figure. The combination is used as a sonometer wire and kept under tension T. The point O is midway between the two bridges. When a stationary wave is set up in the composite wire, the joint is found to be a node. The ratio of the number of antinodes formed in $W_1$ to $W_2$ is :

A standing wave is formed by the superposition of two waves travelling in opposite directions. The transverse displacement is given by
$$y(x,t)=0.5\sin\left(\frac{5\pi}4x\right)\cos(200\pi t).$$
What is the speed of the travelling wave moving in the positive $x$ direction ?

($x$ and t are in meter and second, respectively.)

Two loudspeakers $M$ and $N$ are located 20 m apart and emit sound at frequencies 118 Hz and 121 Hz, respectively. A car is initially at a point $P$, 1800 m away from the midpoint $Q$ of the line $MN$ and moves towards $Q$ constantly at 60 km/hr along the perpendicular bisector of $MN$. It crosses $Q$ and eventually reaches a point $R$, 1800 m away from $Q$. Let $\nu(t)$ represent the beat frequency measured by a person sitting in the car at time $t$. Let $\nu_P$, $\nu_Q$ and $\nu_R$ be the beat frequencies measured at locations $P$, $Q$ and $R$, respectively. The speed of sound in air is $330\ \mathrm{m\,s^{-1}}$. Which of the following statement(s) is(are) true regarding the sound heard by the person?

A uniform string of length 20 m is suspended from a rigid support. A short wave pulse is introduced at its lowest end. It starts moving up the string. The time taken to reach the support is :

(take g = 10 ms$^{-2}$)

A pipe open at both ends has a fundamental frequency $f$ in air. The pipe is dipped vertically in water so that half of it is in water. The fundamental frequency of the air column is now :

Two engines pass each other moving in opposite directions with uniform speed of 30 m/s. One of them is blowing a whistle of frequency 540 Hz. Calculate the frequency heard by driver of second engine before they pass each other. Speed of sound is 330 m/sec :

A toy-car, blowing its horn, is moving with a steady speed of 5 m/s, away from a wall. An observer, towards whom the toy car is moving, is able to hear 5 beats per second. If the velocity of sound in air is 340 m/s, the frequency of the horn of the toy car is close to :

A container of fixed volume has a mixture of one mole of hydrogen and one mole of helium in equilibrium at temperature $T$. Assuming the gases are ideal, the correct statement(s) is(are)

Four harmonic waves of equal frequencies and equal intensities $I_0$ have phase angles 0, $\pi/3$, $2\pi/3$ and $\pi$. When they are superposed, the intensity of the resulting wave is $nI_0$. The value of $n$ is

A train is moving on a straight track with speed 20 ms$^{-1}$. It is blowing its whistle at the frequency of 1000 Hz. The percentage change in the frequency heard by a person standing near the track as the train passes him is (speed of sound = 320 ms$^{-1}$) close to :

A bat moving at 10 ms$^{-1}$ towards a wall sends a sound signal of 8000 Hz towards it. On reflection it hears a sound of frequency $f$. The value of $f$ in Hz is close to (speed of sound = 320 ms$^{-1}$)

A source of sound emits sound waves at frequency $f_0$. It is moving towards an observer with fixed speed $v_s$ ($v_s<v$, where $v$ is the speed of sound in air). If the observer were to move towards the source with speed $v_0$, one of the following two graphs (A and B) will give the correct variation of the frequency f heard by the observer as $v_0$ is changed.

The variation of f with $v_0$ is given correctly by :

One end of a taut string of length 3 m along the $x$ axis is fixed at $x=0$. The speed of the waves in the string is $100\ \mathrm{m\,s^{-1}}$. The other end of the string is vibrating in the $y$ direction so that stationary waves are set up in the string. The possible waveform(s) of these stationary waves is(are)

A student is performing an experiment using a resonance column and a tuning fork of frequency $244\ \mathrm s^{-1}$. He is told that the air in the tube has been replaced by another gas (assume that the column remains filled with the gas). If the minimum height at which resonance occurs is $(0.350\pm0.005)$ m, the gas in the tube is

(Useful information: $\sqrt{167RT}=640\ \mathrm{J^{1/2}\,mole^{-1/2}}$; $\sqrt{140RT}=590\ \mathrm{J^{1/2}\,mole^{-1/2}}$. The molar masses $M$ in grams are given in the options. Take the values of $\sqrt{10/M}$ for each gas as given there.)

A pipe of length 85 cm is closed from one end. Find the number of possible natural oscillations of air column in the pipe whose frequencies lie below 1250 Hz. The velocity of sound in air is 340 m/s.

A transverse wave is represented by :
$$y=\frac{10}{\pi}\sin\left(\frac{2\pi}{T}t-\frac{2\pi}{\lambda}x\right)$$
For what value of the wavelength the wave velocity is twice the maximum particle velocity ?

Two factories are sounding their sirens at 800 Hz. A man goes from one factory to other at a speed of 2 m/s. The velocity of sound is 320 m/s. The number of beats heard by the person in one second will be :

A source of sound A emitting waves of frequency 1800 Hz is falling towards ground with a terminal speed $v$. The observer B on the ground directly beneath the source receives waves of frequency 2150 Hz. The source A receives waves, reflected from ground, of frequency nearly : (Speed of sound = 343 m/s)