a string along which waves can travel is 2.70 m long and has a mass of 260.0 g. the tension in the string is 36.0 n. what must b

Question

2 years ago

10

e the frequency of traveling waves of amplitude 7.70 mm for the average power to be 58.0 w?

1 answer:

stellarik [79] · Answer 1 · 2023-12-28T08:48:20+03:00

By power transmitted by string, the frequency must be 163.31 Hz.

We need to know about power transmitted to solve this problem. The power transmitted by a wave on string can be determined by this equation

P = 1/2 . μ . ω² . A² . v

where P is the power, μ is mass per unit length of string, ω is angular speed, A is amplitude and v is wave propagation speed.

the wave propagation can be determined as

v = √(F.l/m)

where F is the string tension, l is length and m is the mass.

From the question above, we know that:

l = 2.7 m

m = 260 g = 0.26 kg

F = 36 N

A = 7.7 mm = 0.0077 m

P = 58 W

Find the mass per unit length

μ = m / l

μ = 0.26 / 2.7

μ = 0.096 kg / m

Find the wave propagation speed

v = √(F.l/m)

v = √(36. 2.7 /0.26)

v = √(373.85)

v = 19.34 m/s

Find the angular speed

P = 1/2 . μ . ω² . A² . v

58 = 1/2 . 0.096 . ω² . 0.0077² . 19.34

ω² = 1053777.29

ω = √1053777.29

ω = 1026.54 rad/s

Find the frequency

ω = 2πf

1026.54 = 2 . 3.14 . f

f = 163.31 Hz

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