A guitar string with a linear density of 2.0 g/m is stretched between supports that are 60 cm apart. The string is observed to form a standing wave with three antinodes when driven at a frequency of 420 Hz.
Part A
What is the frequency of the fifth harmonic of this string?
Part B
What is the tension in the string?

(a)

(b)

Explanation:

For part (a)

The wave with three antinodes has m=3.Thus f₃=3f₁ and so the fundamental frequency of string is:

Thus the frequency of fifth harmonic is

For Part (b)

The speed  of transverse wave on this string is related to the fundamental frequency by:

As the speed of wave is related to tension of string and its linear density by:

answer: 2×10^-2kg

explanation: density= mass per volume

vol=mass/density

converting to s.i units we have;

3÷1000kg = 0.003

1.5÷100m = 0.15

0.003/0.15 = 0.02kg