Tranverse waves and velocity problem

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The discussion focuses on calculating the speed of transverse waves on a piano string, its tension, and the resulting sound wave properties. The string's length is 1.6 m, mass density is 26 mg/m, and it vibrates at a fundamental frequency of 450 Hz. Key relationships include the wave speed formula, which connects speed, wavelength, and frequency, as well as the tension-mass density-wave speed relationship. Participants seek assistance in solving these physics problems, particularly in determining the wavelength of the fundamental mode and the tension in the string. Understanding these concepts is crucial for accurately solving the problem.
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A piano string of length 1.6 m and mass density 26 mg/m vibrates at a (fundamental) frequency of 450 Hz.

(a) What is the speed of the transverse string waves?
(b) What is the tension?
c) What are the wavelength and frequency of the sound wave in air produced by vibration of the string? The speed of sound in air at room temperature is 340 m/s.

I have been working on this problem and cannot seem to come up with the solution. Any help would be greatly appreciated.
 
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What have you done so far?

What's the wavelength of the fundamental mode? How are speed, wavelength, and frequency related?

What's the relationship between tension, mass density, and wave speed?
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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