A musician plays a string on a guitar that has a fundamental frequency of 330.0

Question

A musician plays a string on a guitar that has a fundamental frequency of 330.0 Hz. The string is 64.2 cm long and has a mass of 0.316 g.
(a) What is the tension in the string?
__________N

(b) At what speed do the waves travel on the string?
__________m/s

(c) While the guitar string is still being plucked, another musician plays a slide whistle that is closed at one end and open at the other. He starts at a very high frequency and slowly lowers the frequency until beats, with a frequency of 5 Hz, are heard with the guitar. What is the fundamental frequency of the slide whistle with the slide in this position?
__________Hz

(d) How long is the open tube in the slide whistle for this frequency?
___________m

Explanation / Answer

Linear density = m/l = 0.316 x 0.001/0.642 = 4.922 x 10^(-4) Kg/m

Wavelength = = 2l (For fundamental mode) = 1.284 m

speed of wave = v = frequecy x wavelength

= 330 x 1.284 = 423.72 m/s

speed = sqrt(tension/linear density)

(a) tension = v^2 = 4.922 x 10^(-4) x 423.72^2 = 90.467 N

(b) speed of wave = 423.72 m/s ( calculated above)

(c) Frequency of pipe = 335 Hz (As beat frequecy = f2 - f1)

(d) Fundamental for open pipe = v/4l = 335

v for air waves = 340 m/s

length for pipe = 340/(4*335) = 0.2537 m = 25.37 cm

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