Waves practice · Medium

Option A is correct because mechanical transverse waves require a medium with shearing properties, which gases lack.

Option D (All of these) is correct because the air column in a pipe closed at one end can resonate at the fundamental frequency and its odd harmonics.

Option C ($\frac{\pi}{2} + (\phi)$) is correct because to find the phase difference, both waves must be expressed as sine functions, and then the difference in their arguments is calculated.

Option B (178.2 Hz) is correct because it is the fundamental frequency calculated using the given density, elasticity, and strain of the steel wire.

Option A ($\frac{2(n+1)}{2 n+1}$) is correct because it represents the ratio of the frequencies of the nth overtone for an open and closed organ pipe of the same length.

Option B ($\frac{{2\pi }}{{3}}$) is correct because the resultant amplitude is equal to the individual amplitudes only when the phase difference is $\frac{{2\pi }}{{3}}$.

Option B (85, closed) is correct because the given frequencies are odd multiples of 85, indicating a closed pipe.

Option B ($64 \mathrm{~cm} \mathrm{~s}^{-1}$ in positive $x$-direction) is correct because the wave velocity is calculated from the coefficients of t and x in the wave equation.

Option A ($819^{\circ} \mathrm{C}$) is correct because the speed of sound is proportional to the square root of the temperature, and doubling the speed requires quadrupling the absolute temperature.

Option B ($V - v$,if $A = \lambda /2\pi$) is correct because the wave velocity equals the maximum particle velocity when the amplitude is equal to the wavelength divided by $2\pi$.

Option D (Both (1) and (2) options are correct) is correct because a Carnot engine operates between two temperatures with maximum efficiency and consists of two isothermal and two adiabatic processes.

Option C (It is the result of superposition of two waves of wavelength $3 {~m}$, frequency $60 {~Hz}$ each travelling with a speed of $180 {~m} / {s}$ in opposite direction) is correct because the given equation represents a stationary wave formed by the superposition of two waves with the specified wavelength, frequency, and speed.

Option C ($\frac{3}{8}\,\,m{s^{ - 1}}$) is correct because it is the velocity of the wave, calculated using the formula v = w/k.

The correct answer is Four times because the frequency of vibration of a string is directly proportional to the square root of the tension.

Option A (1) is correct because the tension in the string is calculated using the formula relating velocity, tension, and mass per unit length.

Option D (Quink's tube experiment is related with beats) is incorrect because Quink's tube experiment is related to interference, not beats.

Option C ($\frac{v}{9}$) is correct because it is derived from the Doppler effect equations for a moving observer and a stationary source.

The correct answer is A because Z₁ and Z₂ represent waves with the same frequency traveling in opposite directions, which is the condition for forming a stationary wave.

Option B (3) is correct because the beat frequency is the absolute difference between the frequencies of the two vibrations.

Option D (3 m, 60 Hz) is correct because the wavelength and frequency are derived from the given standing wave equation.

Option C (beats will be not heard for A and C but will be heard for B) is correct because at A and C, the observer is moving directly towards or away from both sources, while at B, the motion is towards one source and away from the other.

Option C is correct because the intensity of a harmonic wave depends on both its frequency and amplitude.

Option B (Third) is correct because the calculation of the harmonic mode using the given frequency, speed of sound, and pipe length results in n=3.

Option B ($\frac{\lambda}{2}$) is correct because the distance between a compression and an adjacent rarefaction is half the wavelength of the pressure wave.

Option B ($\lambda = 2l$) is correct because the fundamental frequency in an open pipe has a wavelength twice the length of the air column.

Option C (If Assertion is True but the Reason is False) is correct because the assertion about standing waves is true, but the reason stating the amplitude doesn't depend on position is false; the amplitude varies with position in a standing wave.

Option A ($\lambda=2 \pi \times 10^{-2} \mathrm{~m}$) is correct because it is the wavelength calculated using the given amplitude, frequency, and wave speed.

Option B (Apparent frequency will be greater than the real frequency) is correct because the Doppler effect causes an increase in frequency when the observer moves towards the source.

Option C is correct because the total energy (sum of kinetic and potential energy) remains constant during simple harmonic oscillations.

Option D (500) is correct because it is the frequency heard by the observer calculated using the Doppler effect formula when the source is moving towards the observer.