It is not clear to me whether the wire is fixed at either or both ends. I'd guess it's fixed at both. If so, the 'start' is a node, and .32m is the distance from there to the given point.goonking said:A metal wire is vibrating at its third-harmonic frequency. 0.32 m from one end, the amplitude is equal to one quarter the maximum amplitude. Find the length of the wire.
It depends what you mean by x.goonking said:the amplitude going to be 1/4 its maximum where sin(x) = 0.25, correct?
if it helps, the hint the question has is : "The third harmonic will have a wavelength equal to 2/3 of the length of the string. Also, *note to self* the max-amplitude of this wave is (2A) not (A)."haruspex said:It is not clear to me whether the wire is fixed at either or both ends. I'd guess it's fixed at both. If so, the 'start' is a node, and .32m is the distance from there to the given point.
It depends what you mean by x.
So what does that tell you about whether one or both ends of the string are nodes?goonking said:if it helps, the hint the question has is : "The third harmonic will have a wavelength equal to 2/3 of the length of the string. Also, *note to self* the max-amplitude of this wave is (2A) not (A)."
The third harmonic frequency is a term used in physics and engineering to describe the third multiple of the fundamental frequency of a periodic wave. It is also known as the third overtone or the third harmonic.
The third harmonic frequency can be calculated by multiplying the fundamental frequency by 3. For example, if the fundamental frequency is 100 Hz, the third harmonic frequency would be 300 Hz.
The third harmonic frequency is important because it affects the overall shape and quality of a periodic wave. It is also used in the design and analysis of electrical circuits, musical instruments, and other systems that involve periodic waves.
The third harmonic frequency is just one of many harmonics that can be present in a periodic wave. It is the third multiple of the fundamental frequency, while the second harmonic is the second multiple, and so on. The presence and strength of each harmonic can impact the overall properties of the wave.
Yes, the third harmonic frequency can be changed or manipulated through various methods such as adjusting the fundamental frequency, altering the properties of the medium through which the wave travels, or using filters to remove or amplify certain harmonics. This can be useful in applications such as signal processing and sound engineering.