The wavelength is 0.75 m
Explanation:
A standing wave is created on a string when a vibration is imparted on the string, and the string is fixed at the two ends (so that the two ends correspond to two nodes, where the oscillation is zero).
If there are no other nodes in the string, then the string is said to be vibrating at its fundamental frequency. For a string vibrating at its fundamental frequency, the wavelength of the standing wave is equal to twice the length of the string:
[tex]\lambda_1 = 2L[/tex]
where L is the length of the string.
The fundamental frequency is therefore given by
[tex]f_1=\frac{v}{\lambda_1}=\frac{v}{2L}[/tex]
where v is the speed of the wave.
However, in this case the string is vibrating in 4 segments: this means that the string is vibrating at its 4th harmonic (4th mode of vibration). The frequency of the 4th harmonic is given by
[tex]f_4 = 4 f_1 = 4(\frac{v}{2L}) = \frac{2v}{L}[/tex]
And correspondigly, the wavelength of the 4th harmonic is
[tex]\lambda_4 = \frac{v}{f}=\frac{v}{2v/L}=\frac{L}{2}[/tex]
This string has a length of
L = 1.5 m
Therefore, the wavelength when it vibrates in 4 segments is:
[tex]\lambda_4 = \frac{1.5}{2}=0.75 m[/tex]
Learn more about waves:
brainly.com/question/5354733
brainly.com/question/9077368
#LearnwithBrainly
