Waves & Sound — JEE Advanced PYQs

List-I shows four configurations made of straight and semi-circular narrow tubes containing air. A sound wave of wavelength $\lambda =0.29\mathrm{m}$ enters these structures at the point $S$ and a sound detector is placed at $D$. Between the points $S$ and $D$, the sound travels …

Consider a system of three connected strings, $S_1,S_2$ and $S_3$ with uniform linear mass densities $\mu \mathrm{kg}/\mathrm{m}$, $4\mu \mathrm{kg}/\mathrm{m}$ and $16\mu \mathrm{kg}/\mathrm{m}$, respectively, as shown in the figure. $S_1$ and …

An audio transmitter (T) and a receiver (R) are hung vertically from two identical massless strings of length 8 m with their pivots well separated along the $X$ axis. They are pulled from the equilibrium position in opposite directions along the $X$ axis by a small angular am …

Two uniform string of mass per unit length $\mu$ and $4\mu$, and length $L$ and $2L$, respectively, are joined at point O, and tied at two fixed ends P and Q, as shown in the figure. The strings are under a uniform tension T. If we define the frequency …

A source (S) of sound has frequency 240 Hz. When the observer (O) and the source move towards each other at a speed $v$ with respect to the ground (as shown in Case 1 in the figure), the observer measures the frequency of the sound to be 288 Hz. However, when the observer and t …

A string of length 1 m and mass $2\times 10^{-5}\mathrm{kg}$ is under tension T . when the string vibrates, two successive harmonics are found to occur at frequencies 750 Hz and 1000 Hz. The value of tension T is ____ Newton.

$S_1$ and $S_2$ are two identical sound sources of frequency 656 Hz. The source $S_1$ is located at $O$ and $S_2$ moves anti-clockwise with a uniform speed $4\sqrt{2}{\mathrm{ms}}^{-1}$ on a circular path around $O$, as shown in the figure. There are three …

$S_1$ and $S_2$ are two identical sound sources of frequency 656 Hz. The source $S_1$ is located at $O$ and $S_2$ moves anti-clockwise with a uniform speed $4\sqrt{2}{\mathrm{ms}}^{-1}$ on a circular path around $O$, as shown in the figure. There are three …

A source, approaching with speed $u$ towards the open end of a stationary pipe of length $L$, is emitting a sound of frequency $f_{\mathrm{s}}$. The farther end of the pipe is closed. The speed of sound in air is $v$ and $f_0$ is the fundamental frequency of the pipe. …

A stationary tuning fork is in resonance with an air column in a pipe. If the tuning fork is moved with a speed of $2{\mathrm{ms}}^{-1}$ in front of the open end of the pipe and parallel to it, the length of the pipe should be changed for the resonance to occur with the moving tu …

A train S1, moving with a uniform velocity of 108 km/h, approaches another train S2 standing on a platform. An observer O moves with a uniform velocity of 36 km/h towards S2, as shown in figure. Both the trains are blowing whistles of same frequency 120 Hz. When O is 600 m away f …

A musical instrument is made using four different metal strings, 1,2,3 and 4 with mass per unit length $\mu ,2\mu ,3\mu$ and $4\mu$ respectively. The instrument is played by vibrating the strings by varying the free length in between the range ${\mathrm{L}}_0$ and …

A musical instrument is made using four different metal strings, 1,2,3 and 4 with mass per unit length $\mu ,2\mu ,3\mu$ and $4\mu$ respectively. The instrument is played by vibrating the strings by varying the free length in between the range ${\mathrm{L}}_0$ and …

In an experiment to measure the speed of sound by a resonating air column, a tuning fork of frequency $500Hz$ is used. The length of the air column is varied by changing the level of water in the resonance tube. Two successive resonances are heard at air columns of length …

Two men are walking along a horizontal straight line in the same direction. The man in front walks at a speed $1.0m{s}^{-1}$ and the man behind walks at a speed $2.0m{s}^{-1}$. A third man is standing at a height $12m$ above the same horizontal line such that all three men are i …

A block $M$ hangs vertically at the bottom end of a uniform rope of constant mass per unit length. The top end of the rope is attached to a fixed rigid support at $O$. A transverse wave pulse (Pulse 1) of wavelength ${\lambda }_0$ is produced at point $O$ on the rope. The …

A stationary source emits sound of frequency $f_0=492\mathrm{Hz}$. The sound is reflected by a large car approaching the source with a speed of $2{\mathrm{ms}}^{-1}$. The reflected signal is received by the source and superposed with the original. What will be the beat fr …

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 perpendicula …

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 $n{I}_0$. The value of $n$ is

One end of a taut string of length $3m$ along the $x$ axis is fixed at $x=0$. The speed of the waves in the string is $100m{s}^{-1}$. 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( …

A student is performing an experiment using a resonance column and a tuning fork of frequency $244s^{-1}$. 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 …

A horizontal stretched string, fixed at two ends, is vibrating in its fifth harmonic according to the equation, $y(x,t)=(0.01m)\sin \left[\left(62.8m^{-1}\right)x\right]\cos \left[\left(628s^{-1}\right)t\right]$. Assuming $\pi =3.14$, the correct statement(s) is (are) …

Two vehicles, each moving with speed $u$ on the same horizontal straight road, are approaching each other. Wind blows along the road with velocity $w$. One of these vehicles blows a whistle of frequency $f_1$. An observer in the other vehicle hears the frequency of the wh …

A person blows into open-end of a long pipe. As a result, a high-pressure pulse of air travels down the pipe. When this pulse reaches the other end of the pipe,

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 $38^{\circ }\mathrm{C}$ in which the speed of sound is 336 m/s. The zero of the meter scale coincides with t …

A police car with a siren of frequency 8 kHz is moving with uniform velocity 36 km/hr towards a tall building which reflects the sound waves. The speed of sound in air is $320\mathrm{m}/\mathrm{s}$. The frequency of the siren heard by the car driver is

Column I shows four systems, each of the same length L, for producing standing waves. The lowest possible natural frequency of a system is called its fundamental frequency, whose wavelength is denoted as ${\lambda }_{\mathrm{f}}$. Match each system with statements given in Column …

When two progressive waves $y_1=4\sin (2x-6t)$ and $y_2=3\sin \left(2x-6t-\frac{\pi }{2}\right)$ are superimposed, the amplitude of the resultant wave is

A stationary source is emitting sound at a fixed frequency ${\mathrm{f}}_0$, which is reflected by two cars approaching the source. The difference between the frequencies of sound reflected from the cars is 1.2% of ${\mathrm{f}}_0$. What is the difference in the speeds of the car …

A hollow pipe of length 0.8 m is closed at one end. At its open end a 0.5 m long uniform string is vibrating in its second harmonic and it resonates with the fundamental frequency of the pipe. If the tension in the wire is 50 N and the speed of sound is $320{\mathrm{ms}}^{-1}$, t …

A student performed the experiment to measure the speed of sound in air using resonance air-column method. Two resonances in the air-column were obtained by lowering the water level. The resonance with the shorter air-column is the first resonance and that with the longer air-col …

A 20 cm long string, having a mass of 1.0 g, is fixed at both the ends. The tension in the string is 0.5 N. The string is set into vibrations using an external vibrator of frequency 100 Hz . Find the separation (in cm) between the successive nodes on the string.

A transverse sinusoidal wave moves along a string in the positive $x$-direction at a speed of $10\mathrm{cm}/\mathrm{s}$. The wavelength of the wave is 0.5 m and its amplitude is 10 cm. At a particular time $t$, the snap-shot of the wave is shown in figure. The velocity of po …

In the experiment to determine the speed of sound using a resonance column,
(A) prongs of the tuning fork are kept in a vertical plane
(B) prongs of the tuning fork are kept in a horizontal plane
(C) in one of the two resonances observed, the length of the resonating air column i …

A massless rod is suspended by two identical strings AB and CD of equal length. A block of mass m is suspended from point O such that BO is equal to 'x'. Further, it is observed that the frequency of $1^{\text{st }}$ harmonic (fundamental frequency) in AB is equal to …