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Light travels a distance $x$ in time $t_1$ in air and $10x$ in time $t_2$ in another denser medium. What is the critical angle for this medium?
A wave in a string has an amplitude of $2 \text{ cm}$. The wave travels in the +ve direction of x-axis with a speed of $128 \text{ ms}^{-1}$ and it is noted that $5$ complete waves fit in $4 \text{ m}$ length of the string. The equation describing the wave is:
Dimensional formula for angular momentum is
Two periodic waves of intensities $I_1$ and $I_2$ pass through a region at the same time in the same direction. The sum of the maximum and minimum intensities is:
The fundamental frequency of a closed organ pipe of a length $20 \text{ cm}$ is equal to the second overtone of an organ pipe open at both ends. The length of the organ pipe open at both ends will be:
An organ pipe filled with a gas at $27^\circ\text{C}$ resonates at $400\text{ Hz}$ in its fundamental mode. If it is filled with the same gas at $90^\circ\text{C}$, the resonance frequency at the same mode will be:
The driver of a car travelling at a speed of $30 \text{ m/s}$ towards a hill sounds a horn of frequency $600 \text{ Hz}$. If the velocity of sound in air is $330 \text{ m/s}$, the frequency of reflected sound as heard by the driver is:
Which one of the following statements is true?
Two identical piano wires kept under the same tension $T$ have a fundamental frequency of $600 \text{ Hz}$. The fractional increase in the tension of one of the wires which will lead to the occurrence of $6 \text{ beats/s}$ when both the wires oscillate together would be:
A wave traveling in the +ve x-direction having maximum displacement along y-direction as $1 \text{ m}$, wavelength $2\pi \text{ m}$ and frequency of $1/\pi \text{ Hz}$, is represented by:
An electric dipole with dipole moment $4 \times 10^{-9}$ C m is aligned at $30^\circ$ with the direction of a uniform electric field of magnitude $5 \times 10^4$ NC$^{-1}$. The magnitude of the torque acting on the dipole is:
The equation of a simple harmonic wave is given by $y=3\sin\frac{\pi}{2}(50t-x)$ where $x$ and $y$ are in meters and $t$ is in seconds. The ratio of maximum particle velocity to the wave velocity is:
Three sound waves of equal amplitudes have frequencies of $(n-1), n,$ and $(n+1)$. They superimpose to give beats. The number of beats produced per second will be:
Two sound waves with wavelengths $5.0 \text{ m}$ and $5.5 \text{ m}$, respectively, propagate in a gas with a velocity of $330 \text{ m/s}$. How many beats per second can we expect?
$4.0 \text{ gm}$ of gas occupies $22.4 \text{ litres}$ at NTP. The specific heat capacity of the gas at a constant volume is $5.0 \text{ J K}^{-1}\text{mol}^{-1}$. If the speed of sound in the gas at NTP is $952 \text{ ms}^{-1}$, then the molar heat capacity at constant pressure will be: ($R=8.31 \text{ J K}^{-1}\text{mol}^{-1}$)
In Young's double slit experiment, the slits are $2\text{ mm}$ apart and are illuminated by photons of two wavelengths, $\lambda_1 = 12000\text{ \AA}$ and $\lambda_2 = 10000\text{ \AA}$. At what minimum distance from the common central bright fringe on the screen $2\text{ m}$ from the slit will a bright fringe from one interference pattern coincide with a bright fringe from the other?
Two insulated charged copper spheres A and B have their centers separated by a distance of 50 cm. What is the mutual force of electrostatic repulsion if the charge on each is $6.5 \times 10^{-7}$ C? (The radii of A and B are negligible compared to the distance of separation.)
A body is thrown vertically upwards. If the air resistance is to be taken into account, then the time during which the body rises is:
In Young's double-slit experiment, if the separation between coherent sources is halved and the distance of the screen from the coherent sources is doubled, then the fringe width becomes:
A hollow metal sphere of radius R is uniformly charged. The electric field due to the sphere at a distance r from the centre: