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PHYSICS HELP - Newtons, tension, guitar, frequency, etc.?
A guitar string 60.0 centimeters long, with a diameter of 1.40 mm and a tension of 289 N, send a note with a frequency of 147 Hz Find the frequency in each of the following situations. A) The sequence character is reduced by pressing a fret halfway up the chain. B) The voltage is reduced to 196 N. c) A string of the same material, 45.0 cm long and 1.00 mm in diameter with 169 N of tension is pulled. d) The chain produces the third harmonic of 147 Hz fundamental frequency. E) the chain sends the tone of the third your 147 Hz fundamental.
Before you begin to resolve the parties, we must find the wavelength (w0) and velocity (v0) of the sound at the beginning, and the M / L (mass per unit length) string: To find w0: The fundamental frequency is 147 Hz as it relates to the largest wave formed (nodules the ends of the chain, but nowhere else), we w0 = 2 * L = 120 cm = 1.2 m. For v: Use v0 = w0 * f = 1.2 m * 147 Hz to find M / L: Use v0 = sqrt (T / M / L) for m / L = T / v0 ^ 2 = 289 N / (1.2 * 147 m / s) ^ 2 (a) If the rope is shortened, which means the new length is half length age. This will not change the speed of the wave, as the tension and mass per unit length are kept constant. * * This will change the wavelength and therefore frequency. If the string is half its original length, then the longer wavelengths that we have is now w = 60 cm = 0.6 m. This is because w = 2 * L, and L is 30 cm. As V is constant, and v = w * f, we know that if w decreases by a factor of 2, increases in f by the same factor for the new frequency is f = 2 * 147 Hz (b) Figure the new speed using v = sqrt (T / m / L). We calculated m / L at the beginning, so this should be easy. Since chain is the same length, so is the wavelength, then v = w0 * f, and solve f (c) m / L and T are different now. To find m / L, density use. Density is mass / volume => you can find the volume of a cylinder by finding the area of the circle cross-section and multiplying by the length of the cylinder. (Thus, the volume of a cylinder of 5cm diameter 2 inches would be 4 * pi * 1 cm. Alarm units.) Since the density is constant here, you may find the new M / L via: m1/V1 = m2/V2 ==> M2 = M1 * V2/V1 ==> m2/L2 = m1/L1 V2/V1 *. So you can find the new speed. The wave is now different, since the length has changed, but it is still 2 * L (L is now 45 cm), so you can find the frequency, again using v = frequency * Wavelength. (d) The third harmonic instrument to pack in more waves in jail. The only restriction on the waves is that they have to be zero at the edges. You must take the different harmonies to understand them better. This means that one third the wavelength is 2 / 3 * L (as there are 1.5 waves packed in sequence). The nth harmonic, the wavelength is 2 / n * L. Therefore, the frequency in this case is 3 / 2 the original frequency (again as v0 remains the same) (e) This is exactly the same as part (d). I hope it was not too confusing. Good luck!
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