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Please help me to solve this problem!to find the length of the string and to write equation.? 10pts?

• Please help me to solve this problem!to find the length of the string and to write equation.? Vibrations from a 622-Hz tuning fork set up standing waves in a string clamped at both ends. The wave speed for the string is 388m/s. The standing wave has four loops and an amplitude of 1.90mm. What is the length of the string as a function of position and time.

• Answer:

  Well, the amplitude isn't really a factor, so don't worry about it since it only pertains to volume or loudness. Okay, the first thing to do in finding the length of the string is to find the wavelength. The formula is as follows: wavelength = speed/frequency or 388/622Hz which is 0.62m Now, the formula for figuring string length is: wavelength = 2(L)/N. I the wavelength can also be expressed using the Greek Lambda symbol, which I cannot do now. Anyway, the 'N' in the formula represents the number of anit-nodes, which is 4. Therefore, 0.62 = 2(L)/4. This fraction can be simplified to be 0.62 = 1/2(L). Now, since you're figuring for length you must solve for 'L,' so multiply both sides of the equation by the inverse, which is 2/1 or simply 2. Now you have your answer; the length of the string is 1.24m