Waves practice · Mixed difficulty

Option A (Transverse wave) is correct because in transverse waves, the particle's motion is perpendicular to the wave's direction of travel.

Option A ($9$) is correct because intensity is proportional to the square of the pressure amplitude.

Option A is correct because the intensity of sound is directly proportional to the density of the medium.

Option B (0.75) is correct because the length of the closed pipe is calculated by equating the fundamental frequency of the open pipe to the first overtone of the closed pipe.

Option B (Its speed and wavelength increases) is correct because as the wave moves upward, the tension increases, leading to an increase in speed and wavelength.

Option B ($2 {A}_2$) is correct because the difference between the maximum and minimum resultant amplitudes is twice the smaller amplitude.

Option D (at the same time with different velocities) is correct because in a stationary wave, all particles between two nodes reach their mean position simultaneously, but their velocities depend on their distance from the nodes.

Option A is correct. The fundamental frequency of an open organ pipe increases with temperature because the velocity of sound increases more rapidly than the length of the pipe.

Option C ($\frac{{2(p + 1)}}{{2p + 1}}$) is correct because it represents the ratio of the frequencies of the p-th overtones in an open and a closed pipe of the same length.

The system is a tube of air open at one end (Option B) because the resonant frequencies are odd multiples of the fundamental frequency.

Option C ($341.2^\circ C$) is correct because the velocity of sound is proportional to the square root of the absolute temperature.

Option D (Only $I\\;and\\;IV$ are true) is correct because the velocity of sound in air increases with temperature and is independent of pressure.

Option B ($80,240$) is correct because the fundamental frequency is calculated as v/4l and the next higher overtone is three times the fundamental frequency for a tube closed at one end.

Option C (At the point of observation, the amplitudes of two S.H.M. produced by two sources are equal and both the S.H.M. are along the same straight line) is correct because minimum intensity is zero when amplitudes are equal and the waves are in opposite phase.

Option C ($\frac{\sqrt{3} v_0}{2}$) is correct because it is derived from the wave equation and the given condition where displacement is half the maximum value.

Option D ($\sqrt {\frac{P}{\rho }}$) is correct because the speed of sound in a gas is proportional to the square root of the pressure divided by the density.

The correct answer is D (19/18). The ratio of frequencies is calculated using the Doppler effect formula for a moving source approaching a stationary observer, considering the two different speeds of the train.

Option D (4) is correct because the number of beats heard by the observer is the difference between the frequencies heard directly from the source and from its reflection.

Option B (Twice when plucked in the middle) is correct because plucking at 1/4th length creates a higher frequency, specifically twice the frequency when plucked in the middle.

Option A ($\frac{1}{6}\sec$) is correct because the time interval between maximum intensity and the next minimum is half the time period of the beat frequency.

Option A (7) is correct because the number of beats produced is calculated by finding the difference in frequencies after changing the lengths of the pipes.

Option A (200,400,600,800...) is correct because opening the other end of a closed organ pipe doubles the fundamental frequency, and all subsequent harmonics are integer multiples of this new fundamental frequency.

Option C ($300 \mathrm{~m} / \mathrm{s}$) is correct because the speed of sound in air is independent of pressure at a constant temperature.

Option D (None of these) is correct because sound requires a medium to travel and cannot propagate through a vacuum.

Option D ($3.5 \mathrm{~m}$) is correct because it is the wavelength calculated from the wave number (k) in the given electromagnetic wave equation.

Option C (5) is correct because the amplitude of the resultant wave is calculated using the Pythagorean theorem since the two SHMs are perpendicular.

Option B (Both Assertion and Reason are correct but Reason is not the correct explanation of Assertion) is correct because both statements are true, but the reason doesn't explain the assertion.

Option A (Statement-I is correct) is correct because the velocity of sound increases with temperature due to increased molecular kinetic energy.

Option B ($\sqrt{{\frac{{42}}{{25}}}}$) is correct because it correctly applies the formula for the speed of sound in a gas, accounting for the ratio of specific heats and molar masses.

Option B (Increase) is correct because increasing the length of the closed pipe decreases its frequency, thus increasing the beat frequency with the open pipe.