Please help me out. I am very confused so please also explain what youre doing.
ID: 1610479 • Letter: P
Question
Please help me out. I am very confused so please also explain what youre doing.
An E guitar string of length 70 cm is fixed at both ends. Its fundamental frequency (frequency of the fundamental harmonic) is f = 330 Hz.
1) What is the wavelength of the fundamental oscillation of this string?
a. = 175 cm
b. = 35 cm
c. = 70 cm
d. = 105 cm
e. = 140 cm
2) What is the velocity of a wave travelling in the string?
a. v = 684 m/s
b. v = 462 m/s
c. v = 200 m/s
3) The string is retuned. The new tension is T' = 4T. What is the new fundamental frequency of the string, f'?
a. f' = 2f
b. f' = f/4
c. f' = 4f
d. f' = f e. f' = f/2
4) The string is replaced with a new string. The new string has the same length (70 cm) and tension T. It has four times the mass, M'' = 4M. What is the new fundamental frequency of the string, f''?
a. f'' = f/2
b. f'' = 2f
c. f'' = f
d. f'' = 4f
e. f'' = f/4
Explanation / Answer
1) fundamental frequency is f = v/2L ------------ (1)
where v is the speed of the wave, We know that
f = v (for a wave, frequencyXwavelength = speed of wave)
So, = v/f
So from equation (1) we have v/f = 2L = 2(70cm) = 140cm
So = v/f = 140cm
So option e) is correct.
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2) from equation (1) above we have, v = 2Lf = 2(70cm)(330Hz) =2(0.7m)(330Hz) = 462m/s
So, option b) is correct.
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3) For a wave speed of wave v = [T/µ], where T is the tension, µ is mass per unit length of string.
New tension is T' = 4T, putting this value of tension in above formula we get new speed of the wave v',
whre v' = [4T/µ] = 2[T/µ] = 2v, so the speed is doubled, if tension is quadrupled.
Now we know that, fundamental frequency is f = v/2L
So new fundamental frequency is f' = v'/2L = 2v/2L = v/L, thus the fundamnetal frequency is doubled.
So, option a) is correct.
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4) initially, mass per unit length of string µ = M/L
New mass per unit length of string is µ' = 4M/L = 4µ (length is same for both strings)
So the new speed v' = [T/4µ] = (1/2)[T/µ] = v/2
So the new fundamental frequency is f' = v'/2L = (v/2)/2L = f/2
So, option a) is correct.
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This concludes the answers. Check the answer and let me know if it's correct. If you need anymore clarification or correction I will be happy to oblige....