Exam 17: The Principle of Linear Superposition and Interference Phenomena

For a diffraction horn loudspeaker, the sound emerges through a rectangular opening.The width of a diffraction horn is 0.14 m.If the speed of sound in air is 343 m/s, at what frequency is the diffraction angle $\theta$ equal to 35°?

Two traveling pulses on a rope move toward each other at a speed of 1.0 m/s.The waves have the same amplitude.The drawing shows the position of the waves at time t = 0 s.Which one of the following drawings depicts the waves on the rope at t = 2.0 s?

A cylindrical tube sustains a fundamental frequency f₁ when both of its ends are open.A second cylindrical tube with one end closed has the same fundamental frequency.What is the ratio of the length of the second tube to that of the first, L₂/L₁?

A pebble is dropped in a lake; and it produces ripples with a frequency of 0.50 Hz.When should a second pebble be dropped at the same place to produce destructive interference?

17-2 Two loudspeakers are located 3.0 m apart on the stage of an auditorium.A listener at point P is seated 19.0 m from one speaker and 15.0 m from the other.A signal generator drives the speakers in phase with the same amplitude and frequency.The wave amplitude at P due to each speaker alone is A.The frequency is then varied between 30 Hz and 400 Hz.The speed of sound is 343 m/s. -Determine the value of the maximum amplitude in terms of A.

What is the wavelength of the first harmonic?

17-5 A string with a length of 3.0 m has two adjacent resonances at frequencies 112 Hz and 140 Hz. -Determine the wavelength of the 140 Hz resonance.

Water waves approach an aperture.The resulting patterns are shown for two different cases, A and B, in which the wavelength and aperture size are varied. Which one of the following statements concerning these cases is true?

One string on a guitar is exactly in tune.The guitarist uses this string to produce a tone with a frequency of 196 Hz by pressing down at the proper fret.An adjacent string can also be used to produce this tone without being pressed against a fret.However, this adjacent string is out of tune and produces a tone that sounds lower in frequency than the other tone.When the tones are produced simultaneously, the beat frequency is 5.0 Hz.What frequency does the adjacent string produce?

17-5 A string with a length of 3.0 m has two adjacent resonances at frequencies 112 Hz and 140 Hz. -Determine the fundamental frequency of the string.

17-2 Two loudspeakers are located 3.0 m apart on the stage of an auditorium.A listener at point P is seated 19.0 m from one speaker and 15.0 m from the other.A signal generator drives the speakers in phase with the same amplitude and frequency.The wave amplitude at P due to each speaker alone is A.The frequency is then varied between 30 Hz and 400 Hz.The speed of sound is 343 m/s. -At what frequency or frequencies will the listener at P hear a maximum intensity?

17-3 Vibrations with frequency 6.00 × 10² Hz are established on a 1.33-m length of string that is clamped at both ends.The speed of waves on the string is 4.00 × 10² m/s. -How many antinodes are observed for the resulting standing wave pattern?

A rope of length L is clamped at both ends.Which one of the following is not a possible wavelength for standing waves on this rope?

A guitar string produces 4 beats/s when sounded with a 250 Hz tuning fork and 9 beats per second when sounded with a 255 Hz tuning fork.What is the vibrational frequency of the string?

A guitar string has a linear density of 8.30 × 10^-4 kg/m and a length of 0.660 m.The tension in the string is 56.7 N.When the fundamental frequency of the string is sounded with a 196.0-Hz tuning fork, what beat frequency is heard?

17-4 A 6.00-m long string sustains a three-loop standing wave pattern as shown.The wave speed is 2.00 × 10² m/s. -What is the lowest possible frequency for standing waves on this string?

17-6 The figures show standing waves of sound in six organ pipes of the same length.Each pipe has one end open and the other end closed.Note: some of the figures show situations that are not possible. -Which one of the pipes emits sound with the lowest frequency?

17-4 A 6.00-m long string sustains a three-loop standing wave pattern as shown.The wave speed is 2.00 × 10² m/s. -What is the frequency of vibration?

Two pulses of identical shape travel toward each other in opposite directions on a string, as shown in the drawing.Which one of the following statements concerning this situation is true?

17-5 A string with a length of 3.0 m has two adjacent resonances at frequencies 112 Hz and 140 Hz. -Determine the speed of the waves on the string vibrating at 140 Hz..