How Do You Calculate Wave Speed on a String?

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The speed of a wave on a string can be calculated using the formula v = √(T/μ), where T is the tension and μ is the linear density of the string. Given a tension of 110N and a density of 0.09 kg/m, the wave speed can be determined. The frequency of 100Hz and amplitude of 4.5cm are relevant for wave characteristics but do not affect the wave speed calculation directly. The small amplitude indicates that the tension remains constant during wave propagation. Understanding these parameters is crucial for accurately calculating wave speed on a string.
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A string of density \mu=0.09 kg/m is under tension of 110N. A force is supplied to the string to generate a sinusoidal wave at frequency of 100Hz and amplitude of 4.5cm. What is the speed of wave on the string?

I am wondering if I can get the speed of the wave on the string by using v=(T/\mu)? If that is the case, what is the frequency and amplitude use for?
 
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Probably the small amplitude tells that the tension is constant.
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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