A student builds a tunable stringed musical instrument using a fishing line of mass 6 g and length 60 cm. The fishing line slides through a tuning peg that allows the student to adjust the tension. The developed instrument was tested in a room where the speed of sound is 344 m/s. The student adjusts the tension so that when it vibrates in its second overtone, it produces sound with a wavelength of 0.63 m. i) Determine the tension in the fishing line in order to vibrate in the second overtone. ii) Determine the frequency of the sound produced by this line in its fundamental mode of vibration.

Aiming to determine the radius of a 2.5 kg metal ball by investigating the properties of standing waves, a scientist hangs the ball vertically at one end of a string that passes over a light, frictionless pulley. The string's second end is attached to a rigid support, as shown in the figure. The horizontal section of the string vibrates in its second harmonic when the ball is hanging in the air. While it vibrates in its fourth harmonic, the ball is completely submerged in a liquid of density 1.1 g/cm³. The string oscillation frequency is the same before and after the ball is completely submerged in the liquid. Determine the radius of the ball.

Opposing waves with equal frequency and amplitude form a standing wave via interference. The figure below shows a standing wave vibrating on a string with an oscillation frequency of 250 Hz. Calculate the speed at which this wave travels along the string.

Antinodes are points of maximum displacement in standing waves. In the figure below, a standing wave on a string oscillates at a frequency of 200 Hz. If the frequency were to be doubled to 400 Hz, keeping the wave's speed constant how many antinodes would be present in the resulting wave pattern?

A research lab is investigating the properties of an erbium-doped fiber laser (EDFL) for potential applications in telecommunications. The lab has set up an EDFL with a cavity length of 48 cm, configured to oscillate in the 150,000 modes. To better understand the performance of this laser, the researchers need to determine the wavelength and frequency of the laser beam generated by the EDFL. Calculate these parameters for the given erbium-doped fiber laser setup.

When a 2.25-meter-long horizontal string vibrates at 200 Hz, it forms a standing wave exhibiting five loops. Swinging from top to bottom, a maximum displacement of 12 cm is achieved at the center of each loop. Determine the function representing this standing wave.