Assignment:
Part 1
• The displacement from equilibrium caused by a wave on a string is given by y(x, t) = (-0.00185 m)sin[(42.8 m-1)x - (744 s-1)t]. For this wave, what are the following? (a) amplitude? (b) number of waves in 1 m? (c) number of complete cycles in 1 s? (d) wavelength? (e) speed?
• Point A in the figure is 30 cm below the ceiling. Determine how much longer it will take for a wave pulse to travel along wire 1 than along wire 2.
• A string with linear mass density of 0.1 kg/m is under a tension of 107 N. How much power must be supplied to the string to generate a sinusoidal wave of amplitude 3 cm and frequency 116 Hz?
• 15.42. A cowboy walks at a pace of about two steps per second, holding a glass of diameter 11 cm that contains milk. The milk sloshes higher and higher in the glass until it eventually starts to spill over the top. Determine the maximum speed of the waves in the milk.
• A 49-cm-long wire with a mass of 10.8 g is under a tension of 55.5 N. Both ends of the wire are held rigidly while it is plucked. (a) What is the speed of the waves on the wire? (b) What is the fundamental frequency of the standing wave? (c) What is the frequency of the third harmonic?
• Consider a guitar string stretching 84.6 cm between its anchored ends. The string is tuned to play middle C, with a frequency of 256 Hz, when oscillating in its fundamental mode, that is, with one antinode between the ends. If the string is displaced 1.84 mm at its midpoint and released to produce this note, what are the wave speed, v, and the maximum speed, Vmax, of the midpoint of the string?
• The tension in a 2.9-m-long, 1.1-cm-diameter steel cable (ρ = 7800 kg/m3) is 810 N. What is the fundamental frequency of vibration of the cable?
Part 2
• You drop a stone down a well that is 6.65 m deep. How long is it before you hear the splash? The speed of sound in air is 343 m/s.
• The sound level in decibels is typically expressed as β = 10 log(I/I0), but since sound is a pressure wave, the sound level can be expressed in terms of a pressure difference. Intensity depends on the amplitude squared, so the expression is β = 20 log(P/P0), where P0 is the smallest pressure difference noticeable by the ear: P0 = 2. 10-5 Pa. A loud rock concert has a sound level of 109 dB, find the amplitude of the pressure wave generated by this concert.
• Two sources, A and B, emit a sound of a certain wavelength. The sound emitted from both sources is detected at a point away from the sources. The sound from source A is a distance d from the observation point, whereas the sound from source B has to travel a distance of 4λ. What is the largest value of the wavelength, in terms of d, for the maximum sound intensity to be detected at the observation point? (Assume source A is farther from the observation point than source B.) If d = 12.6 m and the speed of sound is 340 m/s, what is the frequency of the emitted sound?
• A plane flies at Mach 1.5, and its shock wave reaches a man on the ground 21 s after the plane passes directly overhead. (a) What is the Mach angle? (b) What is the altitude of the plane? The speed of the plane is 514.5 m/s.
• A standing wave in a pipe with both ends open has a frequency of 444 Hz. The next higher harmonic has a frequency of 626 Hz. (a) Determine the fundamental frequency. (b) How long is the pipe?
• An observer stands between two sound sources. Source A is moving away from the observer, and source B is moving toward the observer. Both sources emit sound of the same frequency. If both sources are moving with a speed, vsound/9, what is the ratio of the frequencies detected by the observer?
• At a distance of 29 m from a sound source, the intensity of the sound is 62 dB. What is the intensity (in dB) at a point 1.9 m from the source? Assume that the sound radiates equally in all directions from the source.
• A source traveling to the right at a speed of 10.80 m/s emits a sound wave at a frequency of 110.0 Hz. The sound wave bounces off of a reflector, which is traveling to the left at a speed of 5.15 m/s. What is the frequency of the reflected sound wave detected by a listener back at the source? (Use 343 m/s as the speed of sound.)