A string of length 2.00 m is stretched between two fixed points with enough tension to make the transverse wave speed 40.0 m/s on the string. What are the wavelength and frequency of: a. the fundamental mode of the standing wave.
b. 1st overtone
c. The 3rd harmonic

Explanation:

The fundamental mode of the standing wave in string is expressed as;

fo

F = V/2L where;

V is the speed of the transverse wave

L is the length of the string

Given

V = 40.0m/s

L = 2.00m

F = 40.0/2(2)

F = 40/4

F = 10Hertz

Hence the fundamental mode of the standing wave is 10Hz

Overtone/harmonics are integral multiples of the fundamental frequency.

Note that 1st overtone is also called second harmonic

Second harmonic  

First overtone F1 = 2F

Second overtone/Third harmonics = 3F

First overtone F1 = 2*10

First overtone = 20Hz

3rd harmonic = 3*10

3rd harmonic = 30Hz