Waves practice · Mixed difficulty

Option D (1.18) is correct because the relative density is calculated by comparing the change in tension (due to buoyancy) when the mass is immersed in water and the unknown liquid.

Option B (Reflection) is correct because an echo is formed when sound waves bounce off a surface and return to the listener.

Option C is correct because resonance occurs when two sources produce sound of the same frequency.

Option A (Longitudinal) is correct because sound waves in gases are always longitudinal, meaning the particle displacement is parallel to the direction of wave propagation.

Option C ($y=A \sin \left(k^2 x^2-\omega^2 t^2\right)$) is correct because it does not satisfy the standard form of a wave equation, where the arguments of the sine function should be linear in both x and t.

Option D (Lissajous figure) is correct because the superposition of two sinusoidal waves at right angles produces a Lissajous figure.

Option A (0.6) is correct because the frequency is inversely proportional to the length of the string, so the new length can be calculated using the ratio of the frequencies.

Option A (Odd harmonics) is correct because a pipe open at one end only supports odd harmonics due to the boundary conditions.

Option A (500) is correct because the frequency of a vibrating string is proportional to the square root of the tension, which is proportional to the mass attached.

Option C (Intensity and frequency) is correct because loudness is related to intensity, and pitch is related to frequency.

Option D (1.25) is correct because the tension must be increased by a factor of 2.25 to keep the frequency constant when the length is increased by 50%.

Option B is correct because the wave equation represents displacement along the x-axis as a function of y and t.

Option A is correct because the amplitude at a distance l/3 from one end in the 3rd overtone is a*sqrt(3)/2, and squaring it gives 9.

Option B ($35\mathrm{ }\,\,Hz$) is correct because it is the calculated fundamental frequency of the stretched wire using the given parameters.

Option A (Pitch (frequency)) is correct because the Doppler effect describes the change in observed frequency (pitch) of a wave due to relative motion between the source and observer.

Option C is correct because it represents a sinusoidal function with both time and position variables, which is characteristic of a wave.

Option C ($n=\frac{v}{\lambda}$) is correct because it represents the fundamental relationship between frequency, wavelength, and velocity of a wave.

Option B (Decreases) is correct because as temperature increases, the speed of sound in the tuning fork decreases, leading to a decrease in frequency.

Option B (The speed of either of component wave) is correct because in the equation of a standing wave, $\omega/k$ represents the speed of the individual waves that interfere to create the standing wave.

Option D (Different frequencies) is correct because beats are produced due to the superposition of two waves with slightly different frequencies.

Option D ($2{l_2} - {l_1}$) is correct because it represents the length of the cord when the work done is 16J, derived from the relationship between work and extension.

Option B ($\frac{{600}}{{13}} \mathrm{{kHz}}$) is correct because it accounts for the Doppler effect twice: once as the submarine approaches and again as the sound reflects back.

Option D (Longitudinal progressive) is correct because sound waves are longitudinal and propagate outwards from the source.

Option D (16.5 m) is correct because it represents the minimum distance required for the echo to be heard distinctly, considering the persistence of hearing.

Option A (A phase change of $180^\circ$ with velocity reversed) is correct because when a wave pulse reflects from a fixed end, it undergoes a phase change of 180 degrees and the direction of velocity is reversed.

Option D ($55^{\circ} {C}$) is correct because the speed of sound is proportional to the square root of the temperature, and by setting the speeds equal, we can solve for the temperature of oxygen.

Option C (One end is open and another end is closed) is correct because the frequencies are odd multiples of the fundamental frequency.

Option A (1) is correct because the beat frequency is half the percentage increase in tension, which translates to 2% of 100 Hz, resulting in 2 Hz or 2 beats per second. Since we're looking for beats in *one* second, and the frequency difference is 2 Hz, the answer is effectively 2/2 = 1 after considering the fundamental frequency relationship.

Option C (A wavelength of $0.5\mathrm{ }\,m$ and travels in $- ve\mathrm{ }\,y$ direction) is correct because the wavelength is calculated from the wave number, and the direction is determined by the sign in the wave equation.

Option D ($10 \mathrm{~Hz}$) is correct because it is the difference between the frequency heard directly from the source and the frequency of the echo, considering the Doppler effect.