Answer:
a) [tex]\lambda=0.935\ \textup{m}[/tex]
b) [tex]f=36.19\approx 36\ \textup{Hz}[/tex]
Explanation:
Given:
String vibrates transversely fourth dynamic, thus n = 4
mass of the string, m = 13.7 g = 13.7 × 10⁻¹³ kg
Tension in the string, T = 8.39 N
Length of the string, L = 1.87 m
a) we know
[tex]L= n\frac{\lambda}{2}[/tex]
where,
[tex]\lambda[/tex] = wavelength
on substituting the values, we get
[tex]1.87= 4\times \frac{\lambda}{2}[/tex]
or
[tex]\lambda=0.935\ \textup{m}[/tex]
b) Speed of the wave (v) in the string is given as:
[tex]v =f\lambda[/tex]
also,
[tex]v=\sqrt\frac{T}{(\frac{m}{L})}[/tex]
equating both the formula for 'v' we get,
[tex]f\lambda=\sqrt\frac{T}{(\frac{m}{L})}[/tex]
on substituting the values, we get
[tex]f\times 0.935=\sqrt\frac{8.39}{(\frac{13.7\times 10^{3}}{1.87})}[/tex]
or
[tex]f=\frac{33.84}{0.935}[/tex]
or
[tex]f=36.19\approx 36\ \textup{Hz}[/tex]
