What is the amplitude of the vertical motion of a segment of the string located at x = 4.000 cm the bridge (the bottom fixed part of the string) is x=0? = 0.4714m 0.000 ou

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please help me on number 3 part g the answer I have is wrong.

3. The C string on a ukulele is fixed at both ends, is 53.34 cm long, and has a linear density of
1.510 x 10-³ kg/m. The string vibrates at the fundamental frequency (first harmonic).
a) What is the longest wavelength that a standing wave on this string can have?
1067m
b) If the fundamental frequency (first harmonic) of this string is 261.6 Hz, what is the speed of the w
along the string?
279.1 m/s
c) What is the tension on the string? F₁ = 117.6 N
d) What is the angular frequency of the wave? w = 1644
s
e) What is the angular wave number of the wave? k = 5890 rom
f)
If the maximum displacement of a small segment of the string at the antinode is 2.560 mm, wri
equation for the displacement (y direction) of any segment of the string as a function of the tim
distance from the end of the string (x direction)? (hint: 2A = 2.560 mm) y = 0.00256 sm (5.8
g) What is the amplitude of the vertical motion of a segment of the string located at x = 4.000 cm
the bridge (the bottom fixed part of the string) is x = 0? = 0.4714m
h) What is the vertical position of the segment of string at x = 4.000 cm at time t = 2.000 s? y
90400
i) What is the second harmonic frequency (n = 2) of this string? ₁₂ 523.2 H 2
j) At the second harmonic, where would you find a node, other than x = 0 cm and x = 53.34
might help to sketch what the second harmonic looks like) o. 2667 m or 26.67
Transcribed Image Text:3. The C string on a ukulele is fixed at both ends, is 53.34 cm long, and has a linear density of 1.510 x 10-³ kg/m. The string vibrates at the fundamental frequency (first harmonic). a) What is the longest wavelength that a standing wave on this string can have? 1067m b) If the fundamental frequency (first harmonic) of this string is 261.6 Hz, what is the speed of the w along the string? 279.1 m/s c) What is the tension on the string? F₁ = 117.6 N d) What is the angular frequency of the wave? w = 1644 s e) What is the angular wave number of the wave? k = 5890 rom f) If the maximum displacement of a small segment of the string at the antinode is 2.560 mm, wri equation for the displacement (y direction) of any segment of the string as a function of the tim distance from the end of the string (x direction)? (hint: 2A = 2.560 mm) y = 0.00256 sm (5.8 g) What is the amplitude of the vertical motion of a segment of the string located at x = 4.000 cm the bridge (the bottom fixed part of the string) is x = 0? = 0.4714m h) What is the vertical position of the segment of string at x = 4.000 cm at time t = 2.000 s? y 90400 i) What is the second harmonic frequency (n = 2) of this string? ₁₂ 523.2 H 2 j) At the second harmonic, where would you find a node, other than x = 0 cm and x = 53.34 might help to sketch what the second harmonic looks like) o. 2667 m or 26.67
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