A cylindrical pipe, closed at both ends, contains air molecules, where the speed of sound is [v] m/s. When the pipe resonates, it forms a standing sound wave inside. The figure shows a snapshot of the standing wave with a wavelength of [lamda] m. When the air in the pipe resonates at its fundamental frequency, calculate the fundamental frequency in hertz (Hz).

A 2.4 kg particle undergoes horizontal oscillation at the end of an ideal spring. The displacement-time graph of its motion is shown in the figure. A = [A] m and t3= 0.2 s. Determine the positive displacement x of the particle when it has one‑third of the maximum speed. Express your answer in meters.

A [m] kg particle oscillates horizontally at the end of an ideal spring. The displacement-time graph of its motion is shown in the figure. A = [A] m and t3= [t3] s. When the particle is located at 50% of the amplitude from the equilibrium position, determine its kinetic energy (K) in joules. [Hint: frequency can be determined from the time-displacement graph.]

A mass is attached to a horizontal ideal spring, undergoing simple harmonic motion. The displacement amplitude is A = [A] m. At a certain time t, the potential energy stored in the spring is [E1] J, and the kinetic energy of the mass is [E2] J. Determine the maximum magnitude of the spring force exerted on the mass (in newtons). [Hint: the maximum force in SHM is Fmax = k × A.]

A string is stretched between two fixed points. When plucked at one end, a transverse wave pulse reaches the other end in [t] s. The mass of a 1-meter length of the string is [mu] kg, and the tension in the string is [F] N. Determine the length of the string in meters.

Objects A and B are made of the same material with a density of [rho1] kg/m³. Object A is fully submerged in an unknown liquid, and object B is placed on top of A such that only a fraction [f] of object B is submerged. Given that the density of the unknown liquid is [rho2] kg/m³ and the volume of object B is [vB] m3, determine the volume (in m³) of object A.

A 0.45 kg mass is resting on a vertically oscillating platform. The platform undergoes simple harmonic motion. The displacement-time graph of the platform’s motion is shown in the figure. t2= [t2] s. Determine the maximum oscillation amplitude that allows the mass to stay in contact with the platform at all times. [Hint: the supporting (normal) force becomes zero when the mass is about to lose contact with the platform. Consider that the maximum force in SHM is Fmax = m × amax.]

 A [L] m long string of a musical instrument has a mass of [m] kg. When the string resonates, it forms a standing wave. The figure shows a snapshot of the standing wave at t = 0. The resulting sound wave in the surrounding air has a wavelength of [lamda] m. Calculate the tension in the string (in Newtons) required to sustain this vibration. The speed of sound wave in air is 340 m/s.

A 2.2 kg mass is attached to a horizontal, massless, ideal spring with a spring constant of 30 N/m. The system undergoes simple harmonic motion, and its velocity-time graph is shown in the figure. v0 = [v0] m/s and t2= [t2] s. Determine the amplitude (A) of oscillation in meters.

A solid cube with a side length of [L] m is completely submerged in an oil-filled container and suspended from a scale by a cable. The density of the cube is [rho2] kg/m³, and the density of the oil is [rho1] kg/m³. What is the reading on the scale (apparent weight) when the cube is fully submerged in the oil? Express your answer in newtons (N).