Sound Waves JEE Main PYQs, 2020 to 2025

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

Consider the sound wave travelling in ideal gases of $\mathrm{He}, \mathrm{CH}_4$, and $\mathrm{CO}_2$. All the gases have the same ratio $\frac{P}{\rho}$, where $P$ is the pressure and $\rho$ is the density. The ratio of the speed of sound through the gases $\mathrm{V}_{\mathrm{He}}: \mathrm{V}_{\mathrm{CH}_4}: \mathrm{V}_{\mathrm{CO}_2}$ is given by

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:

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

A car P travelling at $20 \mathrm{~ms}^{-1}$ sounds its horn at a frequency of $400 \mathrm{~Hz}$. Another car $\mathrm{Q}$ is travelling behind the first car in the same direction with a velocity $40 \mathrm{~ms}^{-1}$. The frequency heard by the passenger of the car $\mathrm{Q}$ is approximately [Take, velocity of sound $=360 \mathrm{~ms}^{-1}$ ]