Section 7 - Wave interference and path length
7.1 The apparatus shown demonstrates
interference of sound waves. A pure tone from
the speaker takes both paths to the listener's
ear, and the resulting difference in path
lengths then creates interference. The length
of one path can be changed by sliding the
adjustable U-shaped tube at the top. You
adjust this tube to find a position that results in
complete destructive interference. From this
point you then measure how far you must pull
the end of the tube up to first hear destructive
interference again. If this distance is 9.20 cm, what is the frequency of the sound that is being used? (Use 343 m/s for the
speed of sound.)Hz
7.2 Two speakers emit sound of identical frequency and amplitude, in phase with each other. The frequency is 415 Hz. If the
speakers are 9.00 meters apart, and you stand on the line directly between them, 3.47 m from one speaker, are you standing
closer to a point of constructive or destructive interference? (Use 343 m/s for the speed of sound.)Constructive
Destructive
7.3 Two speakers are mounted 5.00 meters apart on the ceiling, at a height of 3.05 meters above your ears. You plug up one ear
with a cotton ball, and stand with your other ear directly under the midpoint of a line connecting the speakers. The speakers
emit identical sound waves, which are in phase when they reach your ear. You start walking, remaining directly under the
connecting line, until you first encounter a point of complete destructive interference. You have walked 0.250 meters. What is
the frequency of the sound coming from the speakers? (Use 343 m/s for the speed of sound.)
HzSection 8 - Beats
8.1 Two violinists are playing their "A" strings. Each is perfectly tuned at 440 Hz and under 245 N of tension. If one violinist turns
her peg to tighten her A string to 251 N of tension, what beat frequency will result? Express your answer to the nearest 100th
of a Hz.
Hz
8.2 Two identical strings are sounding the same fundamental tone of frequency 156 Hz. Each string is under 233 N of tension.
The peg holding one string suddenly slips, reducing its tension slightly, and the two tones now create a beat frequency of
three beats per second. What is the new tension in the string that slipped?
N
8.3 Two cellists play their C strings at their fundamental frequency of 65.4 Hz. They are identical strings at the same tension. One
of the cellists plays a glissando (slides her finger down the string) until she has shortened it to an effective length of 15/16 the
length of the other cellist's C string. What beat frequency will result? Express your answer to the nearest tenth of a Hz.
Hz
8.4 Consider the musical note "A above middle C", known as "concert pitch" or "A440." The frequency of this note is 440 Hz by
international agreement. In the chromatic scale, the frequency of a sharp is a factor of 25/24 higher than the note, and the
frequency of a flat is a factor of 24/25 lower. If the "A sharp" and the "A flat" notes corresponding to A440 are played together,
what will be the resulting beat frequency? (State your answer to the nearest Hz.)
Hz
8.5 You hold two tuning forks oscillating at 294 Hz. You give one of the forks to your friend who walks away at 1.50 m/s. What
beat frequency do you hear? Use 343 m/s as the speed of sound and give your answer to the nearest 100th of a Hz.
Hz(^334) Copyright 2007 Kinetic Books Co. Chapter 17 Problems