Intro to Waves Practice Problems
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 (Pav) transmitted by the traveling wave?
A violin's horizontal cord is held in place by two fixed ends: the bridge and the nut. The fundamental frequency of the stationary waves produced is 440 Hz. How long does it take the oscillating cord to go from the maximum positive displacement to the maximum negative displacement at a point located x = λ/4 from the left end?
A wire of length L is stretched between two clamps. The tension in the wire is adjusted until standing waves are observed on the wire. The amplitude and wavelength of the traveling waves are respectively 4 cm and 1.6 m. What is the amplitude of the wire particle located at i) 0.8 m, ii) 0.4 m, and iii) 0.2 m away from the left clamp?
A wire is stretched horizontally between two vertical stems. When it is strummed, the wire vibrates in its fundamental mode at a frequency of 95 Hz. The transverse waves on this stretched wire have a wavelength of 31 cm, a speed of 29.45 m/s, and an amplitude of 5 mm. What are the maximum transverse velocity and the maximum transverse acceleration of the wire particle at x = 15.5 cm, x = 7.75 cm, and x = 3.875 cm from the left stem?
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.
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 loudspeaker emits sound waves uniformly in all directions. The intensity of the sound waves measured with a sound level meter at 10 m from the loudspeaker is 4 × 10-8 W/m2. What would be the intensity of the sound if you placed the sound level meter at 5 meters from the loudspeaker?
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?
At 20 m from a portable generator, the sound intensity is 2 × 10-4 W/m2. The permissible noise intensity limit during the night is 0.5 μW/m2. i) At what distance from habitation should the generator be placed? ii) Calculate the intensity experienced by a person living at a distance twice the minimum distance. iii) What power of sound does the generator produce?
A light wave from a bulb has an intensity of 1.5 × 10-2 W/m2 at 25 m. Suppose the bulb radiates uniformly in all directions. Find the bulb's total power output.