Question

A standing wave on a string of length L = 3 m is described by the following equation: y(x,t) = 0.08 sin⁡(2πx) cos(300πt). The fundamental frequency, f1, is:

25

Answer 1

Gives

Length (L)=3 m

$y(x,t)=0.08sin(2\pi x)cos(300\pi t)\rightarrow(1)$

Fundamental frequency $f_1=?$

$y(x,t)=Asin(k x)cos(wt)\rightarrow(2)$

We know that

$2L=n\lambda$

Put value

$2\times3=n\times1$

$n=6$

$K=\frac{2\pi}{\lambda}$

eqution (1)and(2)comperision

$2\pi=\frac{2\pi}{\lambda}$

$\lambda=1m$

Number of node =6

Wave length=1m

Fundamental frequency $f_1=\frac{\frac{w}{2\pi}}{n}$

Put value

$f_1=\frac{\frac{300\pi}{2\pi}}{6}$

$f_1=25$