Waves & Sound · JEE Main previous year questions

A transverse wave on a string is described by $y=3\sin \left(36t+0.018x+\pi /4\right)$. where $x$, $y$ are in $\mathrm{cm}$ and $t$ in seconds. The least distance between the two successive crests in the wave is ____ $\mathrm{cm}$. (Nearest integer) $(\pi =3.14)$

The equation of a plane progressive wave is given by $y=5\cos \pi \left(200t-\frac{x}{150}\right)$ where $x$ and $y$ are in $\mathrm{cm}$ and $t$ is in second. The velocity of the wave is ____ $m/s$.

1. A.120
2. B.150
3. C.200
4. D.300

Two tuning forks A and B are sounded together giving rise to 8 beats in 2 s. When fork A is loaded with wax, the beat frequency is reduced to 4 beats in 2 s. If the original frequency of tuning fork B is 380 Hz then original frequency of tuning fork A is _________ Hz.

The velocity of sound in air is doubled when the temperature is raised from $0^{\circ }\text{C}$ to ${\alpha }^{\circ }\text{C}$. The value of $\alpha$ is _____.

The amplitude and phase of a wave that is formed by the superposition of two harmonic travelling waves, $y_1(x,t)=4\sin (kx-\omega t)$ and $y_2(x,t)=2\sin (kx-\omega t+\frac{2\pi }{3})$, are: (Take the angular frequency of initial waves same as $\omega$)

1. A.$\left[\sqrt{3},\frac{\pi }{6}\right]$
2. B.$\left[2\sqrt{3},\frac{\pi }{6}\right]$
3. C.$\left[6,\frac{2\pi }{3}\right]$
4. D.$\left[6,\frac{\pi }{3}\right]$

Consider the sound wave travelling in ideal gases of $\mathrm{He}$, $\mathrm{C}{\mathrm{H}}_4$, and $\mathrm{C}{\mathrm{O}}_2$. All the gases have the same ratio $\frac{P}{\rho }$, where $P$ is the pressure and $\rho$ is the density. The ratio of the speed of sound through the gases $V_{\mathrm{He}}:V_{\mathrm{C}{\mathrm{H}}_4}:V_{\mathrm{C}{\mathrm{O}}_2}$ is given by

1. A.$\sqrt{\frac{7}{5}}:\sqrt{\frac{5}{3}}:\sqrt{\frac{4}{3}}$
2. B.$\sqrt{\frac{5}{3}}:\sqrt{\frac{4}{3}}:\sqrt{\frac{4}{3}}$
3. C.$\sqrt{\frac{5}{3}}:\sqrt{\frac{4}{3}}:\sqrt{\frac{7}{5}}$
4. D.$\sqrt{\frac{4}{3}}:\sqrt{\frac{5}{3}}:\sqrt{\frac{7}{5}}$

In an experiment with a closed organ pipe, it is filled with water by $(\frac{1}{5})$ th of its volume. The frequency of the fundamental note will change by

1. A.$20\%$
2. B.$25\%$
3. C.$-20\%$
4. D.$-25\%$

In the resonance experiment, two air columns (closed at one end) of $100\mathrm{cm}$ and $120\mathrm{cm}$ long, give $15$ beats per second when each one is sounding in the respective fundamental modes. The velocity of sound in the air column is:

1. A.$370m/s$
2. B.$340m/s$
3. C.$335m/s$
4. D.$360m/s$

A closed and an open organ pipe have same lengths. If the ratio of frequencies of their seventh overtones is $\left(\frac{a-1}{a}\right)$ then the value of $a$ is ________.

A plane progressive wave is given by $y=2\cos 2\pi (330t-x)\mathrm{m}$. The frequency of the wave is :

1. A.$660\mathrm{Hz}$
2. B.$340\mathrm{Hz}$
3. C.$330\mathrm{Hz}$
4. D.$165\mathrm{Hz}$

In the given electromagnetic wave ${\mathrm{E}}_y=600\sin (\omega t-\mathrm{k}x){\mathrm{Vm}}^{-1}$, intensity of the associated light beam is (in $W/{\mathrm{m}}^2$) : (Given ${ϵ}_0=9\times 10^{-12}{\mathrm{C}}^2{\mathrm{N}}^{-1}{\mathrm{m}}^{-2}$ )

1. A.486
2. B.729
3. C.243
4. D.972

Two open organ pipes of lengths $60\text{ cm}$ and $90\text{ cm}$ resonate at $6^{\text{th}}$ and $5^{\text{th}}$ harmonics respectively. The difference of frequencies for the given modes is ________ $\text{Hz}$. (Velocity of sound in air $=333\text{ m/s}$)

The equation of stationary wave is : $y=2\mathrm{a}\sin \left(\frac{2\pi \mathrm{nt}}{\lambda }\right)\cos \left(\frac{2\pi x}{\lambda }\right)$. Which of the following is NOT correct :

1. A.The dimensions of $nt$ is $[\mathrm{L}]$
2. B.The dimensions of $n$ is $[{\mathrm{LT}}^{-1}]$
3. C.The dimensions of $x$ is $[\mathrm{L}]$
4. D.The dimensions of $n/\lambda$ is $[\mathrm{T}]$

A tuning fork resonates with a sonometer wire of length $1\mathrm{m}$ stretched with a tension of $6\mathrm{N}$. When the tension in the wire is changed to $54\mathrm{N}$, the same tuning fork produces 12 beats per second with it. The frequency of the tuning fork is ____ $\mathrm{Hz}$.

The fundamental frequency of a closed organ pipe is equal to the first overtone frequency of an open organ pipe. If length of the open pipe is $60\mathrm{cm}$, the length of the closed pipe will be:

1. A.15 cm
2. B.60 cm
3. C.45 cm
4. D.30 cm

The speed of sound in oxygen at S.T.P. will be approximately: (given, $R=8.3\mathrm{J}{\mathrm{K}}^{-1},\gamma =1.4$)

1. A.341 m/s
2. B.333 m/s
3. C.325 m/s
4. D.315 m/s

In a closed organ pipe, the frequency of fundamental note is $30\text{ Hz}$. A certain amount of water is now poured in the organ pipe so that the fundamental frequency is increased to $110\text{ Hz}$. If the organ pipe has a cross-sectional area of $2{\text{ cm}}^2$, the amount of water poured in the organ tube is _________ g. (Take speed of sound in air is $330\text{ m/s}$)

A closed organ pipe $150\text{ cm}$ long gives 7 beats per second with an open organ pipe of length $350\text{ cm}$, both vibrating in fundamental mode. The velocity of sound is _______ $\text{m/s}$.

For a certain organ pipe, the first three resonance frequencies are in the ratio of $1:3:5$ respectively. If the frequency of fifth harmonic is $405\text{ Hz}$ and the speed of sound in air is $324{\text{ ms}}^{-1}$ the length of the organ pipe is _________ $\text{m}$.

A car P travelling at $20{\text{ ms}}^{-1}$ sounds its horn at a frequency of $400\text{ Hz}$. Another car Q is travelling behind the first car in the same direction with a velocity $40{\text{ ms}}^{-1}$. The frequency heard by the passenger of the car Q is approximately [Take, velocity of sound $=360{\text{ ms}}^{-1}$]

1. A.$485\text{ Hz}$
2. B.$514\text{ Hz}$
3. C.$421\text{ Hz}$
4. D.$471\text{ Hz}$

A transverse harmonic wave on a string is given by $$y(x,t)=5\sin (6t+0.003x)$$ where x and y are in cm and t in sec. The wave velocity is ____________ ${\text{ms}}^{-1}$.

For a periodic motion represented by the equation $$y=\sin \omega t+\cos \omega t$$ the amplitude of the motion is

1. A.1
2. B.$\sqrt{2}$
3. C.0.5
4. D.2

An organ pipe $40\text{ cm}$ long is open at both ends. The speed of sound in air is $360{\text{ ms}}^{-1}$. The frequency of the second harmonic is ___________ $\text{Hz}$.

A person driving car at a constant speed of $15\text{ m/s}$ is approaching a vertical wall. The person notices a change of $40\text{ Hz}$ in the frequency of his car's horn upon reflection from the wall. The frequency of horn is ________ $\text{Hz}$. (Given: Speed of sound : $330\text{ m/s}$)