What are the wavelengths of the first four harmonics for this string

1. A string of length 48.0 cLm= is fixed at both ends. It oscillates in a four-loop standing
wave pattern (the 4th harmonic) at a frequency 4 360. fHz= . The tension on the
string is 120.0 Nτ = .
a. What are the wavelengths of the first four harmonics for this string, 1 2 3 4 , , , λ λ λ λ ?
b. What is the wave speed, v, on the string?
c. What is the mass of this string, m?
d. What frequency, 1f, is needed to excite the first harmonic?
e. For a 4n= standing wave on this string, what is the maximum transverse velocity,
( ( , ))Maxuxt , at one of the anti-nodes if one of the two traveling waves that make up
the standing wave has an amplitude 1.25mymm= ?
f. For a 4n= standing wave on this string, what is the maximum transverse acceleration,
( ( , ))tMaxaxt , at one of the anti-nodes if one of the two traveling waves that make up
the standing wave has an amplitude 1.25mymm= ?
g. Sketch the envelope of oscillations for the 1st through 4th harmonics (the shape of the
wave function when cos( ) 1tω = and when cos( ) 1tω = − ) and label the nodes (with
the letter N) and antinodes (with the letter A) on your sketch. Also label the x and y
axes and the points 0x= and xL= on the x axis.

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