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

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

Step-by-step 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*3.14*450`

`\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*0.690*10^(-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*0.690*10^(-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.