I have three questions relating to wave physics

[th3chieftain]

A piano tuner detects that the "middle C" note, which should be 261.6 Hz, is too low by 11.7 Hz. If the original tension was 744 N, what must it be adjsuted to so the note plays the correct frequency?



A wave on a large cable, of mass per unit length 1.52 kg/m, is generated by a machine providing 201 W of power. It produces waves of wavelength 2.23 m and amplitude 1.52 m. What is the speed of these waves?

A string is made of two materials of different mass per unit length, 2.33 g/m on the left and 3.31 g/m on the right, connected together at the center. If the wavelength of the wave on the left segment is 22.4 m, what is the wavelength on the right?

 

[anathema]

I can help you with both of these problems.

For the first problem, we can use the equation v = √(T/μ) to find the new tension needed to produce the correct frequency. Here, v represents the speed of the wave, T is the tension, and μ is the mass per unit length. Rearranging the equation, we get T = μv^2. Plugging in the given values, we get T = (1.52 kg/m)(261.6 Hz)^2 = 104,140 N. This is the tension needed for the correct frequency. Since the original tension was 744 N, we need to increase the tension by 103,396 N to get the correct frequency.

For the second problem, we can use the equation v = fλ, where v is the speed of the wave, f is the frequency, and λ is the wavelength. We are given the frequency (f = 201 W) and wavelength (λ = 2.23 m), so we can solve for the speed. Plugging in the values, we get v = (201 W)/(2.23 m) = 90.27 m/s. This is the speed of the wave on the cable.

For the third problem, we can use the equation v = √(T/μ) again. However, since the string is made of two different materials with different mass per unit length, we need to find the effective mass per unit length (μ) of the entire string. This can be found by taking the average of the mass per unit length on the left and right sides. So, μ = (2.33 g/m + 3.31 g/m)/2 = 2.82 g/m. Now, we can use the same equation as before to find the speed of the wave on the right segment. Plugging in the new mass per unit length and the given wavelength (λ = 22.4 m), we get v = √(2.82 g/m)(f/λ) = √(2.82 g/m)(261.6 Hz)/22.4 m) = 4.02 m/s. This is the speed of the wave on the right segment. Since the frequency (f) is the same on both segments, we can use the equation v = fλ to find the wavelength on the right segment. Pl