Waves — JEE Main PYQs

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

($\pi = 3.14$)

A sinusoidal wave of wavelength 7.5 cm travels a distance of 1.2 cm along the $x$-direction in 0.3 sec. The crest P is at $x=0$ at $t=0$ sec and maximum displacement of the wave is 2 cm. Which equation correctly represents this wave ?

In the resonance experiment, two air columns (closed at one end) of 100 cm and 120 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:

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

Displacement of a wave is expressed as $x(\mathrm{t}) = 5\cos\left(628\mathrm{t} + \dfrac{\pi}{2}\right)$ m. The wavelength of the wave when its velocity is 300 m/s is :

($\pi = 3.14$)

Two harmonic waves moving in the same direction superimpose to form a wave $x = a\ \cos(1.5t)\ \cos(50.5t)$ where t is in seconds. Find the period with which they beat. (close to nearest integer)

The equation of a wave travelling on a string is $y = \sin[20\pi x + 10\pi t]$, where $x$ and $t$ are distance and time in SI units. The minimum distance between two points having the same oscillating speed is :

Two strings with circular cross section and made of same material, are stretched to have same amount of tension. A transverse wave is then made to pass through both the strings. The velocity of the wave in the first string having the radius of cross section R is $v_1$, and that in the other string having radius of cross section R/2 is $v_2$. Then $\frac{v_2}{v_1} =$

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 $y_2(x, t) = 2\sin\left(kx - \omega t + \frac{2\pi}{3}\right)$, are:

(Take the angular frequency of initial waves same as $\omega$)

A closed organ and an open organ tube are filled by two different gases having same bulk modulus but different densities $\rho_1$ and $\rho_2$, respectively. The frequency of $9^{th}$ harmonic of closed tube is identical with $4^{th}$ harmonic of open tube. If the length of the closed tube is 10 cm and the density ratio of the gases is $\rho_1 : \rho_2 = 1 : 16$, then the length of the open tube is :

The equation of a transverse wave travelling along a string is $y(x, t) = 4.0 \sin\left[20 \times 10^{-3} x + 600 t\right]$ mm, where $x$ is in mm and $t$ is in second. The velocity of the wave is :

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R

Assertion A: A sound wave has higher speed in solids than gases.

Reason R: Gases have higher value of Bulk modulus than solids.

In the light of the above statements, choose the correct answer from the options given below

A sonometer wire of resonating length 90 cm has a fundamental frequency of 400 Hz when kept under some tension. The resonating length of the wire with fundamental frequency of 600 Hz under same tension ________ cm.

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

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 :

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

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

A point source is emitting sound waves of intensity $16 \times 10^{-8}\ Wm^{-2}$ at the origin. The difference in intensity (magnitude only) at two points located at a distances of $2m$ and $4m$ from the origin respectively will be _______ $\times\ 10^{-8}\ Wm^{-2}$.

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 cm, the length of the closed pipe will be:

The speed of sound in oxygen at S.T.P. will be approximately:

(given, $R = 8.3\ \mathrm{JK^{-1}}$, $\gamma = 1.4$)