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
The concept of amplitude is maximum displacement or distance moved by a point on a waver about the point of equibrilium.
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
Converting level 8dB to the intensity
On the other hand,
A 25-cm-long wire with a linear density of 20 g/m passes across the open end of an 85-cm-long open-closed tube of air. If the wire, which is fixed at both ends, vibrates at its fundamental frequency, the sound wave it generates excites the second vibrational mode of the tube of air. What is the tension in the wire? Assume vsound = 340 m/s.
Biologists think that some spiders “tune” strands of their web to give an enhanced response at frequencies corresponding to those at which desirable prey might struggle. Orb spider web silk has a typical diameter of 20 µm, and spider silk has a density of 1300 kg/m3. To have a fundamental frequency at 100 Hz, to what tension must a spider adjust a 12-cm-long strand of silk?
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