Apiano wire with mass 3.00 g and length 80.0 cm is stretched with a tension of 25.0 n. a wave with frequency 120.0 hz and amplitude 1.6 mm travels along the wire.
(a) calculate the average power carried by the wave.
(b) what happens to the average power if the wave amplitude is halved.

(a) = 0.22 W

(b) = 0.056 W

Explanation:

given information:

the mass of piano wire, m = 3.00 g = 0.003 kg

tension, F = 25 N

length, l = 80 cm = 0.8 m

frequency, f = 120 Hz

amplitude, A = 1.6 mm = 0.0016 m

(a) the average power carried by the wave,

= (√μF)ω²A²

where,

ω = 2πf = 2π120 = 754

μ =

  =

  = 0.00375 kg/m

thus,

= (√(0.00375)(25))(754)²(0.0016)²

= 0.22 W

(b) What happens to the average power if the wave amplitude is halved.

based on the equation above, we know that the average power is proportional to the square amplitude. therefore

=

= 0.056 W

emily ruth's annual premium is $1058.50

step-by-step explanation:

emily ruth is a female of 27 years age purchasing 20 year endowment insurance with face value $25000.

from the given table,

for females, the age of a male 3 years younger should be used.

so, we have to check for 24 year male for 20 year endowment.

it is 42.34 for every $1000 face value.

for a face value of $25000,

it is 25 * 42.34 = $1058.50

∴ emily ruth's annual premium is $1058.50

when two balls of the different masses are dropped from equal height, they reach the ground at the same time .this is because they experience the same acceleration.

the acceleration is independent of mass.

thus when they are dropped they will always maintain the same velocity and travel the same distance (neglect air resistance of course) at the same time.