#2 #4#10#12#16#18#20#22#242. What is the frequency of a tuning fork vibrating with a period of 0.0008 s?
Remembering that the period and frequency of an oscillator are related as the inverse of each other, we get
4. How long is a wavelength of infrasound with a frequency of 2 Hz?
The speed of sound in air is about 343 m/s. Using the relationship that the wavelength times the frequency equals the speed of sound, we get
10. If the "shot heard around the world" could actually travel around the world, how long would it take? (Assume that the circumference of the earth is 40,000 km.)
The time that it would take the sound to actually travel around the world (or one circumference of the earth) can be gotten from the distance equation. Using 40,000 km for the circumference of the earth gives
12. How deep is a school of fish if the sonar echo is received 0.2 s after it was sent?
In this problem, remember that the sound wave must travel from the boat to the depth, d, of the fish and return to be recorded. So, the sound traveled a total distance 2d in 0.2 s. This gives us
16. If the fundamental frequency of a guitar string is 440 Hz, what harmonic frequencies are possible?
A guitar string is fixed at both ends, so its fundamental wavelength is twice its length. Other possible harmonics will have a whole number of half-wavelengths on the string. (Draw a picture to convince yourself of this.) The corresponding frequencies will be multiples, by the same whole number, of the fundamental. We see this from
and so on...
18. What is the fundamental frequency for a 60-cm banjo string if the speed of waves on the string is 264 m/s?
The fundamental wavelength is twice the length of the banjo string, or
120 cm = 1.2 m. Since the speed of the waves is 264 m/s, we obtain
20. What frequencies are possible in an open organ pipe that is 1.5 m long?
An open organ pipe has two free ends. The fundamental wavelength is twice the length of the pipe, or 3.0 m. Each higher harmonic requires one additional node added to the previous number of nodes, beginning with the one node in the fundamental. Since a half-wavelength is the distance between two consecutive nodes, each successive harmonic has an additional half-wavelength in the organ pipe. Thus, the harmonics increase by consecutive whole numbers of half-wavelengths in the organ pipe. That is
22. How long is an open organ pipe with a fundamental frequency of 512 Hz?
The fundamental wavelength of an open organ pipe is twice the pipe's length. For a fundamental frequency of 512 Hz, we get
So, the length of the open organ pipe is 33.5 cm.
24. What is the beat frequency of two piano wires that vibrate at 440 Hz and 444 Hz?
The beat frequency is the difference between the two wave frequencies, so f = 444 Hz - 440 Hz = 4 Hz.