Assignment:
Problems:
1) A sound wave from your speakers playing The Charming Beggars has a frequency of 262 Hz and travels with a velocity of 330 m/s. How far apart are the wave crests (compressions)?
2) Greezy-X is in his fishing boat on the Kankakee River. He notices wave crests that pass the bow of his anchored boat every 3 s. He measures the distance between the crests to be 7.5 m. What is the velocity of the waves?
3) A wave traveling in the positive x direction has a frequency of 25 Hz. See the diagram for other information. Find the (a) amplitude, (b) wavelength, (c) period, (d) velocity of the wave, (e) write out the wave equation for the wave, and (f) calculate the maximum transverse speed of the wave.
4) Two waves, one of amplitude 0.3 m and the other of amplitude 0.4 m are traveling towards each other.
(a) What is the largest resultant amplitude of these two waves when they meet?
(b) What is the smallest resultant amplitude of these two waves when they meet?
(c) Under what conditions will the answers to (a) and (b) occur?
5) While tuning his guitar, Mitch hears one beat every 0.25 s when comparing two strings. One of the strings is sounding a true "C" note which is 262 Hz. What could the possible frequencies be of the other string?
6) Transverse waves are traveling at a velocity of 30 m/s on a rope that has a tension of 9 N. If the tension on the string is increased to 22 N what will be the new velocity of the waves?
7) The 3rd and 5th harmonics that sound when a guitar string is struck are 1152 Hz and 1920 Hz. The string is 65 cm long and is under 300 N of tension. (a) What is the fundamental frequency for this string? (b) Find the mass per unit length of the string.
8) A string of 3 g/m is fixed at both ends. A standing wave of frequency 2000 Hz is set up in which the nodes are 8 cm apart.
(a) What is the wavelength of the standing wave?
(b) Calculate the velocity of the waves.
(c) What is the tension of the string?
9) A rope of length 8 m and mass 40 g is fixed at both ends. The tension of the rope is 49 N.
(a) What are the positions of the nodes and the antinodes for the 3rd harmonic?
(b) Calculate the frequency for this harmonic.