Q. 47

Expert-verified
Found in: Page 485

Physics for Scientists and Engineers: A Strategic Approach with Modern Physics

Book edition 4th
Author(s) Randall D. Knight
Pages 1240 pages
ISBN 9780133942651

A vibrating standing wave on a string radiates a sound wave with intensity proportional to the square of the standing-wave amplitude. When a piano key is struck and held down, so that the string continues to vibrate, the sound level decreases by 8.0 dB in 1.0 s. What is the string’s damping time constant t?

The constant damping time of the string is

See the step by step solution

Step 1: Description of vibration and amplitude

The concept of amplitude is maximum displacement or distance moved by a point on a waver about the point of equibrilium.

Step 2: The explanation of the provided information and solution

Provided information,

The solution to the equation is,

The vibration of the piano does not tend to be constant on the oscillating system that is responsible for decreasing the aptitude that changes over time. the gradual approach of the aptitude is 0. The expression shows the decay.

The A is amplitude, t is time and the time constant is

Step 3: Converting sound to the sound intensity

Converting level 8dB to the intensity

On the other hand,

Therefore,