91影视

1. Frequency of oscillation of diaphragm$f=440\text{鈥塇锄}$
2. Maximum displacement of diaphragm

$\begin{array}{l}{x}_m\text{=0.75鈥尘尘}\\ {\text{=0.75脳10}}^{\text{-3}}\text{m}\end{array}$

Use the fact that an oscillating loudspeaker diaphragm executes Simple Harmonic Motion.

The angular frequency is given as-

$蝇=2蟺\text{f}$

The maximum velocity is given as-

${\text{v}}_{max}=蝇{\text{x}}_m$

The maximum acceleration is given as-

${\text{a}}_{max}={蝇}^2{\text{x}}_m$

The frequency of oscillation (f) of diaphragm is related to angular frequency (蝇) by the relation,

$蝇=2蟺\text{f}$

Putting the values, we get

$\begin{array}{rcl}蝇& =& 2蟺\text{f}\\ & =& 2脳3.14脳440\text{Hz}\\ & =& 2.8脳{10}^3\text{rad/s}\\ & & \end{array}$

For an SHM, maximum speed of oscillations is given by${\text{v}}_{max}=蝇{\text{x}}_m$

Putting the values, we get

$\begin{array}{l}{\text{v}}_{max}=蝇{\text{x}}_m\\ =2.8脳{10}^3\text{鈥塺补诲}/\text{s}脳0.75脳{10}^{鈭�3}\text{鈥尘}\\ =2.1\text{鈥尘}/\text{s}\end{array}$

The maximum velocity is$2.1\text{鈥尘}/\text{s}$.

For SHM, the magnitude of maximum acceleration is given by$a_{max}={蝇}^2{x}_m$

Putting the values,

$\begin{array}{l}{\text{a}}_{max}={蝇}^2{\text{x}}_m\\ ={(2.8脳{10}^{3\text{鈥�}}\text{鈥塺补诲}/\text{s})}^2脳(0.75脳{10}^{鈭�3}\text{鈥尘})\\ =5.7脳{10}^3\text{鈥尘}/{\text{s}}^2\end{array}$

The maximum acceleration is given as$5.7脳{10}^3\text{鈥尘}/{\text{s}}^2$-.