Power Supplied to a vibrating string

In summary, the conversation discusses a problem involving a taut spring with a tension of 80.0N and a coefficient of linear density of 0.05 kg/m. The goal is to find the power needed to generate sinusoidal waves at a frequency of 60Hz and an amplitude of 6cm. After converting the amplitude to meters and using the equations for angular frequency, velocity, and power, the attempted solution yields an answer with incorrect units. The conversation then suggests checking the calculation for velocity.
  • #1
Willjeezy
29
0

Homework Statement


I keep getting the wrong answer for this question:

A taut spring for which μ = 0.05 kg/m is under tension of 80.0N. How much power must be supplied to the string to generate sinusoidal waves at a frequency of 60Hz and an amplitude of 6cm?


Homework Equations


ω = 2∏f
v = √(T/μ)
P = (1/2)μω2A2v

The Attempt at a Solution


Convert cm to m --> 6cm = 0.06m

Find ω
ω = 2∏(60)
= 376.99

Find v
v = √(80/.05)
=0.4m/s2

Find P
P = (1/2)(0.05)(376.99)2(0.06)2(0.4)
=5.12

however, the book tells me the answer is 512W. Did I convert something wrong?

Watts is J/s, and joules is in (Kg * m2)/s, so it only makes sense that I would have to convert the cm to m.

By dimensional analysis my answer has the units of :
(kg * rad2 * m2) / s3
 
Last edited:
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  • #2
Willjeezy said:
Find v
v = √(80/.05)
=0.4m/s2
Check this part of your calculation.
 
  • #3
blah...thanks.
 

Related to Power Supplied to a vibrating string

1. What is "Power Supplied to a vibrating string"?

"Power Supplied to a vibrating string" refers to the amount of energy that is transferred to a string when it is set in motion and begins to vibrate. This energy is necessary to maintain the vibration and produce sound.

2. How is power supplied to a vibrating string?

Power is supplied to a vibrating string through an external force or energy source, such as plucking, striking, or bowing the string. This force causes the string to vibrate and energy is transferred to the string, thus supplying power to it.

3. What factors affect the power supplied to a vibrating string?

The power supplied to a vibrating string is affected by several factors, including the amplitude of the vibration, the tension and length of the string, and the type and amount of force applied to the string.

4. How does the power supplied to a vibrating string affect the sound produced?

The power supplied to a vibrating string directly affects the loudness and intensity of the sound produced. The greater the power supplied, the louder and more intense the sound will be.

5. How is the power supplied to a vibrating string measured?

The power supplied to a vibrating string is typically measured in units of watts, which represent the rate at which energy is transferred to the string. This measurement can be calculated using the formula P = (1/2)mv^2w, where P is power, m is mass, v is velocity, and w is angular frequency.

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