Question

A loudspeaker diaphragm is oscillating in simple harmonic motion with a frequency of 450 Hz and a maximum displacement of 0.690 mm. What are the (a) angular frequency, (b) maximum speed, and (c) magnitude of the maximum acceleration

Answer 1

Answer:

The angular frequency, maximum speed and maximum acceleration are 2826 rad/s, 1.95 m/s and 5510.53 m/s².

Explanation:

Given that,

Frequency = 450 Hz

Amplitude = 0.690 mm

(I). We need to calculate the angular frequency

Using formula of angular frequency

$\omega=2\pi f$

Put the value into the formula

$\omega=2\times3.14\times450$

$\omega=2826\ rad/s$

(II). We need to calculate the maximum speed

Using formula of the maximum speed

$v_{max}=\omega A$

Where, A = amplitude

Put the value into the formula

$v_{max}=2826\times0.690\times10^{-3}$

$v_{max}=1.95\ m/s$

(III). We need to calculate the magnitude of the maximum acceleration

Using formula of the maximum acceleration

$\alpha_{max}=\omega^2 A$

Put the value into the formula

$\alpha_{max}=(2826)^2\times0.690\times10^{-3}$

$\alpha_{max}=5510.53\ m/s^2$

Hence, The angular frequency, maximum speed and maximum acceleration are 2826 rad/s, 1.95 m/s and 5510.53 m/s².