1. A string of length L = 0.720 m is fixed at both ends. It oscillates in a five-loop standing wave pattern at a frequency f, = 625 Hz . The mass of the string is m =3.60 g . a. What is the wavelength of the five-loop pattern (the 5th harmonic), 15, for this string? b. What is the wave speed, v, on the string? c. What is the tension, t for this string? d. What frequency, fi, is needed to excite the first harmonic? e. For a n = 3 standing wave on this string, what is the maximum transverse velocity, Max(u(x,t)) , at one of the anti-nodes if one of the two traveling waves that make up the standing wave has an amplitude y, =1.75mm ? f. Sketch the envelope of oscillations for the 1st through 4th harmonics (the shape of the wave function when cos(@t) =1 and when cos(@t)=-1) and label the nodes (with the letter N) and antinodes (with the letter A) on your sketch.
1. A string of length L = 0.720 m is fixed at both ends. It oscillates in a five-loop standing wave pattern at a frequency f, = 625 Hz . The mass of the string is m =3.60 g . a. What is the wavelength of the five-loop pattern (the 5th harmonic), 15, for this string? b. What is the wave speed, v, on the string? c. What is the tension, t for this string? d. What frequency, fi, is needed to excite the first harmonic? e. For a n = 3 standing wave on this string, what is the maximum transverse velocity, Max(u(x,t)) , at one of the anti-nodes if one of the two traveling waves that make up the standing wave has an amplitude y, =1.75mm ? f. Sketch the envelope of oscillations for the 1st through 4th harmonics (the shape of the wave function when cos(@t) =1 and when cos(@t)=-1) and label the nodes (with the letter N) and antinodes (with the letter A) on your sketch.
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I need help with parts e and f please. I know that a) 0.288m, b) 180 m/s, c) 162 N, and d) 125Hz.
Transcribed Image Text:1. A string of length L = 0.720 m is fixed at both ends. It oscillates in a five-loop standing wave
pattern at a frequency f, = 625 Hz . The mass of the string is m = 3.60 g .
a. What is the wavelength of the five-loop pattern (the 5th harmonic), 15, for this string?
b. What is the wave speed, v, on the string?
c. What is the tension, 7 for this string?
d. What frequency, f, is needed to excite the first harmonic?
e. For a n = 3 standing wave on this string, what is the maximum transverse velocity,
Max(u(x,t)) , at one of the anti-nodes if one of the two traveling waves that make up
the standing wave has an amplitude y, =1.75mm ?
f. Sketch the envelope of oscillations for the 1$t through 4th harmonics (the shape of the
wave function when cos(@ t) =1 and when cos(@t) =-1) and label the nodes (with
the letter N) and antinodes (with the letter A) on your sketch.
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