Question

A piano wire with mass 2.95 g and length 79.0 cmis stretched with a tension of 25.0 N . A wave with frequency 100 Hz and amplitude 1.50 mm travels along the wire.

Part A

Calculate the average power carried by the wave.

Part B

What happens to the average power if the wave amplitude is halved?

Answer 1

Given:

Mass (m) = 2.95 g = 2.95 x 10^-3 kg

Length (L) = 79 cm = 0.79 m

Linear mass density () = m/L = 3.734 x 10^-3 kg/m

Tension (T) = 25 N

Frequency (f) = 100 Hz

Amplitude (A )= 1.5 mm = 1.5 x 10 ^-3 m

Since: Speed of the wave (v) = = = 81.824 m/s

So. Angular frequency () = 2f = 628.32 rad/s

So. Power (P) = (1/2) ² A ² v = (0.5)(3.734 x 10^-3) x (628.32)² x (1.5 x 10^-3) ² x (81.824) = 0.136 W

Part (b) Ans: if A ' = A /2

From above equation P ' / P = (A ' / A) ² = (1/2) ² = 1/4

Therefore: P ' = (1/4) P = 0.0339 W