Exam 16: Superposition and Standing Waves

A string that is 0.15 m long and fixed at both ends is vibrating in its n = 5 harmonic. The sound from this string excites a pipe that is $0.82 \mathrm {~m}$ long and open at both ends into its second overtone resonance. What is the distance between a node and an adjacent antinode, in the string? The speed of sound in air is 345 m/s.

Consider a pipe of length L that is open at one end and closed at the other end. What are the wavelengths of the three lowest-pitch tones produced by this pipe?

A guitar string 0.65 m long has a tension of 61 N and a mass per unit length of 3.0 g/m. (a)What is the speed of waves on the string when it is plucked? (b)What is the string's fundamental frequency of vibration when plucked? (c)At what other frequencies will this string vibrate?

Two loudspeakers placed 6.00 m apart are driven in phase by an audio oscillator having a frequency range from 1595 Hz to 2158 Hz. A point P is located 4.70 m from one loudspeaker and 3.60 m from the other speaker. The speed of sound in the room is 344 m/s. At what frequency (or frequencies)of the oscillator does the sound reaching point P interfere destructively? (There could be more than one correct choice.)

Find the first three harmonics of a string of linear mass density 2.00 g/m and length 0.600 m when the tension in it is 50.0 N.

Two police cars have identical sirens that produce sound of frequency of 570 Hz. A stationary listener is standing between two cars. One car is parked and the other is approaching the listener and both have their sirens on. The listener measures 9.0 beats per second. Find the speed of the approaching police car. The speed of sound is 340 m/s.