A string of mass 5 g and length 1.25 m is tightly attached to a mechanical vibrator at one end and to a fixed support at the other end. The mechanical vibrator generates traveling waves. The traveling wave is modeled with the wave function y = 6 mm (sin { [1.5π (rad/m) x] + [90π (rad/s) t] } ). What is the i) tension (T) in the string and the ii) average power (P_av) transmitted by the traveling wave?

In a physics experiment, two sinusoidal waves are generated along a stretched string, each with the same frequency. The experiment records that one wave carries 1.6 times the power of the other. Calculate the ratio of their amplitudes.

A fire alarm system produces a loud sound that has an intensity of 5 × 10^-2 w/m² at a distance of 4 m. The alarm is on for 15 minutes. What is the energy transferred away from the alarm if its output power remains constant?

A powerful sound emitter is placed at the center of nuclear disposal to prohibit intrusion. The emitter sends sound waves uniformly in all directions. The minimum sound intensity at which an individual starts to feel pain is 1 W/m². If an intruder measures the intensity of 0.25 W/m² at 1 km, how close to the nuclear disposal could the intruder get before the noise became unbearable?

In a sound testing experiment, a loudspeaker is positioned on the horizontal axis. A sound wave of the same intensity could be heard simultaneously by the people standing at x = -12.0 m and x = 20.0 m along the horizontal axis. Determine the exact position of the loudspeaker on the horizontal axis.

A tuning fork produces a sound with a frequency of 440 Hz in air, where the speed of sound is 343 m/s. What is the wavelength of the sound wave produced by the tuning fork?

A wire is strained at 145 N, and its mass per unit length is 0.008 kg/m. A sine wave sent on the wire has an amplitude of 4.5 cm and a wavelength of 1.3 m. Find the greatest speed of a mass element on the wire.

During a laboratory experiment, a group of students observes the formation of a progressive wave along a string using a simple harmonic oscillator. The string has a length of 1.2 m and a mass of 5 g. The progressive wave function y(x, t) is given by y = 8 mm (sin {[3π (rad/cm) x] - [33π (rad/s) t] } ). The teacher asks the student to find out the i) speed (v), ii) and direction of propagation of the progressive wave.

You set up two wires with different linear mass densities, as shown below. Wire A has a linear mass density of 0.15 kg/m. The linear mass density of wire B is 0.05 kg/m. If two waves are simultaneously sent through the wires and are to arrive simultaneously on the opposite end, calculate the required wire lengths L_A and L_B.

A boat is tied to the coast by a 0.85 kg rope. The length of the rope is 5.6 m between the lashing points of the coast and the boat. A sudden jerk of the boat due to the ocean waves creates a transverse wave in the rope, which travels along the rope and reaches the lashing point at the coast in 0.95 s. Find the tension in the rope.

An online tune generator creates sine sound waves in the air with a displacement amplitude of 0.04 mm at f₁ = 200 Hz and f₂ = 20 kHz. What is the pressure amplitude (p_max) at each frequency?  Specify, under these conditions, if these sound frequencies are harmful to human hearing. The pressure variation that corresponds to the harm threshold is 30 Pa.